Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22611725 | C2 | semidirect |
| 5. #22608044 | C2 | semidirect |
| 6. #22608013 | C2 | semidirect |
| 7. C4×#108×C73 | C2 | semidirect |
| 15. #17988402 | C4 | semidirect |
| 16. #17988399 | C4 | semidirect |
| 146. C4×#108 | D73 | semidirect |
| 149. C73 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611725 | 2 |
| #22611678 | 2 |
| #22611658 | 2 |
| #22610819 | 2 |
| #22608044 | 2 |
| #22608013 | 2 |
| C4×#108×C73 | 2 |
| #13137 | 73 |