Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D181 | C2 | semidirect |
| 4. #26041538 | C2 | semidirect |
| 5. #26041537 | C2 | semidirect |
| 6. #26041534 | C2 | semidirect |
| 7. #26041519 | C2 | semidirect |
| 8. #26041518 | C2 | semidirect |
| 9. #26041314 | C2 | semidirect |
| 10. #26041286 | C2 | semidirect |
| 11. #470×C181 | C2 | semidirect |
| 133. C181 | #3059 | semidirect |
| 141. #470 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D181 | 2 |
| C2×#19153824 | 2 |
| #26041852 | 2 |
| #26041538 | 2 |
| #26041537 | 2 |
| #26041534 | 2 |
| #26041519 | 2 |
| #26041518 | 2 |
| #26041314 | 2 |
| #26041286 | 2 |
| #470×C181 | 2 |
| #3059 | 181 |