Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 108 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. C8×C4⋊#64408 | C2 | semidirect |
| 4. #22625145 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624821 | C2 | semidirect |
| 14. #17989446 | C4 | semidirect |
| 15. #17989445 | C4 | semidirect |
| 22. #17988665 | C4 | semidirect |
| 23. #17988664 | C4 | semidirect |
| 25. C8×D292 | C4 | semidirect |
| 30. C8×D4×C73 | C4 | semidirect |
| 208. C73 | #8257 | semidirect |
| 216. C8×D4 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#64408 | 2 |
| #22625428 | 2 |
| #22625310 | 2 |
| #22625145 | 2 |
| #22624827 | 2 |
| #22624821 | 2 |
| #22618638 | 2 |
| #8257 | 73 |