Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 254 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. #22625512 | C2 | semidirect |
| 2. D8×#10596833 | C2 | semidirect |
| 3. #22624965 | C2 | semidirect |
| 4. #22624886 | C2 | semidirect |
| 5. #22624885 | C2 | semidirect |
| 6. #22624842 | C2 | semidirect |
| 35. #14556532 | C8 | semidirect |
| 56. D584 | C2×C8 | semidirect |
| 62. #11924003 | C2×C8 | semidirect |
| 65. D8×C73 | C2×C8 | semidirect |
| 119. C73 | #12045 | semidirect |
| 163. D8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625512 | 2 |
| D8×#10596833 | 2 |
| #22624965 | 2 |
| #22624886 | 2 |
| #22624885 | 2 |
| #22624842 | 2 |
| #22611775 | 2 |
| #12045 | 73 |