Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
772 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 194 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. #22626102 | C2 | semidirect |
| 2. #22626007 | C2 | semidirect |
| 4. #22625672 | C2 | semidirect |
| 5. #22625648 | C2 | semidirect |
| 67. C2×Dic146 | M16 | semidirect |
| 163. C73 | #23271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626102 | 2 |
| #22626007 | 2 |
| #22625911 | 2 |
| #22625672 | 2 |
| #22625648 | 2 |
| #22612470 | 2 |
| #23271 | 73 |