Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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. #22626287 | C2 | semidirect |
| 4. #108×#64408 | C2 | semidirect |
| 5. #22625010 | C2 | semidirect |
| 6. #22624974 | C2 | semidirect |
| 23. #17988404 | C4 | semidirect |
| 24. #17988402 | C4 | semidirect |
| 25. #17988400 | C4 | semidirect |
| 26. #361×C73 | C4 | semidirect |
| 161. C73 | #13137 | semidirect |
| 177. #361 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626287 | 2 |
| #22626246 | 2 |
| #22626084 | 2 |
| #108×#64408 | 2 |
| #22625010 | 2 |
| #22624974 | 2 |
| #22611677 | 2 |
| #13137 | 73 |