Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 15. #17988335 | C4 | semidirect |
| 16. #17988332 | C4 | semidirect |
| 146. C73 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610908 | 2 |
| #22608701 | 2 |
| #22608589 | 2 |
| #22608333 | 2 |
| #22607828 | 2 |
| #22607764 | 2 |
| C4×C4⋊C8×C73 | 2 |
| #9579 | 73 |