Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041641 | C2 | semidirect |
| 3. #26041636 | C2 | semidirect |
| 4. #26041287 | C2 | semidirect |
| 6. C4×#15668433 | C2 | semidirect |
| 7. #533×C181 | C2 | semidirect |
| 15. #19153739 | C22 | semidirect |
| 17. #19153727 | C22 | semidirect |
| 18. C4×#13089678 | C22 | semidirect |
| 19. C4⋊Q8×C181 | C22 | semidirect |
| 20. #125×C181 | C22 | semidirect |
| 83. C181 | #3140 | semidirect |
| 85. #533 | D181 | semidirect |
| 95. C4⋊Q8 | C2×D181 | semidirect |
| 96. #125 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153804 | 2 |
| #26041641 | 2 |
| #26041636 | 2 |
| #26041287 | 2 |
| #26041283 | 2 |
| C4×#15668433 | 2 |
| #533×C181 | 2 |
| #3140 | 181 |