Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22626274 | C2 | semidirect |
| 2. #22626173 | C2 | semidirect |
| 3. #22626158 | C2 | semidirect |
| 4. #22626152 | C2 | semidirect |
| 26. C2×#11924031 | D4 | semidirect |
| 145. C73 | #13200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626274 | 2 |
| #22626173 | 2 |
| #22626158 | 2 |
| #22626152 | 2 |
| #22618626 | 2 |
| #13200 | 73 |