Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 13. #17989449 | C4 | semidirect |
| 14. #17989448 | C4 | semidirect |
| 17. #17988340 | C4 | semidirect |
| 18. #17988339 | C4 | semidirect |
| 19. #335×C73 | C4 | semidirect |
| 91. C8×C73 | #97 | semidirect |
| 94. #10596831 | #97 | semidirect |
| 118. C73 | #8276 | semidirect |
| 130. #335 | #64408 | semidirect |
| 207. C8 | #14556645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625718 | 2 |
| C4×#14556645 | 2 |
| #22625473 | 2 |
| #22624760 | 2 |
| #335×D73 | 2 |
| #8276 | 73 |