Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19153849 | C2 | semidirect |
| 2. C2×#19153824 | C2 | semidirect |
| 4. #26041855 | C2 | semidirect |
| 5. #26041538 | C2 | semidirect |
| 6. #26041526 | C2 | semidirect |
| 7. #26041521 | C2 | semidirect |
| 8. #26041509 | C2 | semidirect |
| 9. #26041273 | C2 | semidirect |
| 10. C2×#19153739 | C2 | semidirect |
| 11. #428×C181 | C2 | semidirect |
| 77. M16×C181 | D4 | semidirect |
| 143. C181 | #3063 | semidirect |
| 153. #428 | D181 | semidirect |
| 210. M16 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153824 | 2 |
| #26041860 | 2 |
| #26041855 | 2 |
| #26041538 | 2 |
| #26041526 | 2 |
| #26041521 | 2 |
| #26041509 | 2 |
| #26041273 | 2 |
| C2×#19153739 | 2 |
| #428×C181 | 2 |
| #3063 | 181 |