Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 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×#19153839 | C2 | semidirect |
| 2. C2×#19153824 | C2 | semidirect |
| 3. #26041859 | C2 | semidirect |
| 4. #26041534 | C2 | semidirect |
| 5. #26041533 | C2 | semidirect |
| 6. #26041532 | C2 | semidirect |
| 7. #26041511 | C2 | semidirect |
| 8. #26041510 | C2 | semidirect |
| 9. #106×D181 | C2 | semidirect |
| 10. #26041279 | C2 | semidirect |
| 11. #470×C181 | C2 | semidirect |
| 65. C8×D181 | D4 | semidirect |
| 139. C181 | #3060 | semidirect |
| 145. #470 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×#19153824 | 2 |
| #26041859 | 2 |
| #26041534 | 2 |
| #26041533 | 2 |
| #26041532 | 2 |
| #26041511 | 2 |
| #26041510 | 2 |
| #106×D181 | 2 |
| #26041279 | 2 |
| #470×C181 | 2 |
| #3060 | 181 |