Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #26041761 | C2 | semidirect |
| 3. #26041392 | C2 | semidirect |
| 4. #26041390 | C2 | semidirect |
| 5. #26041386 | C2 | semidirect |
| 6. C4×#15668436 | C2 | semidirect |
| 7. #26041364 | C2 | semidirect |
| 8. #106×D181 | C2 | semidirect |
| 9. #26041279 | C2 | semidirect |
| 10. #26041236 | C2 | semidirect |
| 11. #441×C181 | C2 | semidirect |
| 13. #19153839 | C4 | semidirect |
| 41. #15668450 | C2×C4 | semidirect |
| 49. #15668436 | C2×C4 | semidirect |
| 50. D1448 | C2×C4 | semidirect |
| 54. C8×D181 | C2×C4 | semidirect |
| 65. Q16×C181 | C2×C4 | semidirect |
| 114. C181 | #2952 | semidirect |
| 121. #441 | D181 | semidirect |
| 165. Q16 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| #26041761 | 2 |
| #26041392 | 2 |
| #26041390 | 2 |
| #26041386 | 2 |
| C4×#15668436 | 2 |
| #26041364 | 2 |
| #106×D181 | 2 |
| #26041279 | 2 |
| #26041236 | 2 |
| #441×C181 | 2 |
| #2952 | 181 |