Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 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×#19153848 | C2 | semidirect |
| 2. #26041941 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041526 | C2 | semidirect |
| 5. #26041501 | C2 | semidirect |
| 6. #26041436 | C2 | semidirect |
| 7. #26041427 | C2 | semidirect |
| 8. #26041358 | C2 | semidirect |
| 9. C4×Q16×C181 | C2 | semidirect |
| 64. Q16×C181 | D4 | semidirect |
| 117. C181 | #3277 | semidirect |
| 126. C4×Q16 | D181 | semidirect |
| 170. Q16 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153848 | 2 |
| #26041941 | 2 |
| #26041663 | 2 |
| #26041526 | 2 |
| #26041501 | 2 |
| #26041436 | 2 |
| #26041427 | 2 |
| #26041358 | 2 |
| C4×Q16×C181 | 2 |
| #3277 | 181 |