Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
784 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 202 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. #22626104 | C2 | semidirect |
| 2. #22626005 | C2 | semidirect |
| 4. #22625668 | C2 | semidirect |
| 5. #22625648 | C2 | semidirect |
| 163. C73 | #23273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626104 | 2 |
| #22626005 | 2 |
| #22625904 | 2 |
| #22625668 | 2 |
| #22625648 | 2 |
| #22612478 | 2 |
| #23273 | 73 |