Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19153837 | C2 | semidirect |
| 2. #26041949 | C2 | semidirect |
| 3. #26041932 | C2 | semidirect |
| 4. #26041505 | C2 | semidirect |
| 5. #26041486 | C2 | semidirect |
| 6. #26041471 | C2 | semidirect |
| 7. #26041438 | C2 | semidirect |
| 8. #26041423 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. C8×D724 | C2 | semidirect |
| 11. #492×C181 | C2 | semidirect |
| 57. #15668438 | D4 | semidirect |
| 127. C4×C181 | #135 | semidirect |
| 140. C181 | #3284 | semidirect |
| 145. #492 | D181 | semidirect |
| 272. C4 | #19153837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153837 | 2 |
| #26041949 | 2 |
| #26041932 | 2 |
| #26041505 | 2 |
| #26041486 | 2 |
| #26041471 | 2 |
| #26041438 | 2 |
| #26041423 | 2 |
| C4×#15668438 | 2 |
| C8×D724 | 2 |
| #492×C181 | 2 |
| #3284 | 181 |