Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22625519 | C2 | semidirect |
| 3. #22624962 | C2 | semidirect |
| 4. #22624888 | C2 | semidirect |
| 6. #22624842 | C2 | semidirect |
| 36. #14556536 | C8 | semidirect |
| 55. Dic292 | C2×C8 | semidirect |
| 67. C16×C73 | C2×C8 | semidirect |
| 113. C73 | #12043 | semidirect |
| 173. C16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625519 | 2 |
| #22625512 | 2 |
| #22624962 | 2 |
| #22624888 | 2 |
| #22624886 | 2 |
| #22624842 | 2 |
| #22611782 | 2 |
| #12043 | 73 |