Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22626138 | C2 | semidirect |
| 2. #22625476 | C2 | semidirect |
| 3. #22624888 | C2 | semidirect |
| 4. #22624885 | C2 | semidirect |
| 30. #14556610 | C8 | semidirect |
| 70. Dic292 | C2×C8 | semidirect |
| 91. D8×C73 | C2×C8 | semidirect |
| 157. C73 | #11592 | semidirect |
| 224. D8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| #22625476 | 2 |
| #22624888 | 2 |
| #22624885 | 2 |
| C4×#14556610 | 2 |
| #11592 | 73 |