Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
724 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×#88111 | C2 | semidirect |
| 3. #13130012 | C2 | semidirect |
| 4. #13129709 | C2 | semidirect |
| 6. C2×C4×D4×C13 | C4 | semidirect |
| 15. #11718882 | C4 | semidirect |
| 18. #11718634 | C4 | semidirect |
| 21. C4×C4⋊Dic13 | C4 | semidirect |
| 22. #11718292 | C4 | semidirect |
| 55. (C2×#261)⋊C4 | C2×C4 | semidirect |
| 57. #88111 | C2×C4 | semidirect |
| 191. C2×C4×D4 | #261 | semidirect |
| 349. C13 | #8220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#88111 | 2 |
| C2×#11718292 | 2 |
| #13130012 | 2 |
| #13129709 | 2 |
| C4×#88192 | 2 |
| #8220 | 13 |