Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D13 |
| commutator, cosocle | C23×C13 | C25 |
| Frattini | C23 | C24×D13 |
| Fitting | C2×C13×#383 | C2 |
| socle | C24×C13 | C24 |
| hypercenter | C2×#383 | D13 |
| hypocenter | C13 | C2×#2818 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C2×#383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#88128 | C2 | semidirect |
| 2. C22×#88130 | C2 | semidirect |
| 3. #13122879 | C2 | direct (N × H) |
| 4. C2×#11718333 | C2 | semidirect |
| 5. C2×#11718332 | C2 | semidirect |
| 6. C2×C13×#383 | C2 | semidirect |
| 14. C2×#88130 | C22 | semidirect |
| 16. C2×#88128 | C22 | semidirect |
| 17. C13×#383 | C22 | semidirect |
| 19. #11718333 | C22 | semidirect |
| 20. #11718332 | C22 | semidirect |
| 31. C2×C42×C13 | D4 | semidirect |
| 64. C42×C13 | C2×D4 | semidirect |
| 73. C2×#383 | D13 | semidirect |
| 109. #383 | C2×D13 | semidirect |
| 143. C2×C42 | D52 | semidirect |
| 146. C2×C13 | #2818 | semidirect |
| 175. C42 | C2×D52 | semidirect |
| 176. C13 | C2×#2818 | semidirect |
| 216. C2 | #13122879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88128 | 2 |
| C22×#88130 | 2 |
| #13122879 | 2 |
| C2×#11718333 | 2 |
| C2×#11718332 | 2 |
| C2×C13×#383 | 2 |
| C2×#2818 | 13 |