Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #22611678 | C2 | semidirect |
| 3. #22611668 | C2 | semidirect |
| 4. #22611560 | C2 | semidirect |
| 5. #22609986 | C2 | semidirect |
| 6. #22608038 | C2 | semidirect |
| 7. C2×#365×C73 | C2 | semidirect |
| 61. M32×C73 | D4 | semidirect |
| 180. C2×#365 | D73 | semidirect |
| 186. C73 | #13400 | semidirect |
| 234. M32 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619594 | 2 |
| #22611678 | 2 |
| #22611668 | 2 |
| #22611560 | 2 |
| #22609986 | 2 |
| #22608038 | 2 |
| C2×#365×C73 | 2 |
| #13400 | 73 |