Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3294 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Fitting | C13×#2842 | C2 |
| prime radical | C25×D13 | C22 |
| hypercenter | #2842 | D13 |
| hypocenter | C13 | C2×#2842 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2842 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13123101 | C2 | semidirect |
| 2. #13123100 | C2 | semidirect |
| 3. #13123099 | C2 | semidirect |
| 4. D13×#399 | C2 | semidirect |
| 5. D13×#396 | C2 | semidirect |
| 7. C13×#2842 | C2 | semidirect |
| 9. C2×C4⋊C4×D13 | C22 | semidirect |
| 12. C13×#399 | C22 | semidirect |
| 13. C13×#396 | C22 | semidirect |
| 16. #11718655 | C22 | semidirect |
| 17. #11718653 | C22 | semidirect |
| 20. #11718610 | C22 | semidirect |
| 21. #11718609 | C22 | semidirect |
| 22. #11718338 | C22 | semidirect |
| 23. #11718337 | C22 | semidirect |
| 24. D13×#95 | C22 | semidirect |
| 33. C2×C13×C4⋊C4 | C23 | semidirect |
| 40. C2×C4⋊Dic13 | C23 | semidirect |
| 41. C2×#6101 | C23 | semidirect |
| 45. C13×#95 | C23 | semidirect |
| 46. #88071 | C23 | semidirect |
| 81. #2842 | D13 | direct (N × H) |
| 119. #399 | C2×D13 | semidirect |
| 123. #396 | C2×D13 | semidirect |
| 159. C2×C4⋊C4 | C22×D13 | semidirect |
| 169. #95 | C22×D13 | semidirect |
| 176. D13 | #2842 | direct (N × H) |
| 207. C13 | C2×#2842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13123101 | 2 |
| #13123100 | 2 |
| #13123099 | 2 |
| D13×#399 | 2 |
| D13×#396 | 2 |
| D13×#379 | 2 |
| C13×#2842 | 2 |
| C2×#2842 | 13 |