Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×Dic362 | C2 | semidirect |
| 2. #26041590 | C2 | semidirect |
| 3. #26041571 | C2 | semidirect |
| 4. #26041476 | C2 | semidirect |
| 5. #26041417 | C2 | semidirect |
| 6. #26041379 | C2 | semidirect |
| 7. #26041336 | C2 | semidirect |
| 66. Dic362 | #41 | semidirect |
| 111. C181 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic362 | 2 |
| #26041590 | 2 |
| #26041571 | 2 |
| #26041476 | 2 |
| #26041417 | 2 |
| #26041379 | 2 |
| #26041336 | 2 |
| #532×C181 | 2 |
| #3112 | 181 |