Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 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×#2840 | C2 |
| hypercenter | #2840 | D13 |
| hypocenter | C13 | #36675 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13123027 | C2 | semidirect |
| 2. #13122920 | C2 | semidirect |
| 3. #13122833 | C2 | semidirect |
| 4. #13118118 | C2 | semidirect |
| 5. #13118053 | C2 | semidirect |
| 6. #13117335 | C2 | semidirect |
| 7. C13×#2840 | C2 | semidirect |
| 9. C22×#6131 | C22 | semidirect |
| 11. C2×Q8×Dic13 | C22 | semidirect |
| 16. #11718892 | C22 | semidirect |
| 17. #11718890 | C22 | semidirect |
| 24. #11718335 | C22 | semidirect |
| 25. #11718333 | C22 | semidirect |
| 26. #11718327 | C22 | semidirect |
| 27. #11718321 | C22 | semidirect |
| 28. #11718309 | C22 | semidirect |
| 58. C24×C13 | #41 | semidirect |
| 86. #2840 | D13 | semidirect |
| 188. C24 | #6131 | semidirect |
| 215. C13 | #36675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13123027 | 2 |
| #13122920 | 2 |
| #13122833 | 2 |
| #13118118 | 2 |
| #13118053 | 2 |
| #13117335 | 2 |
| C13×#2840 | 2 |
| #36675 | 13 |