Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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. #26041712 | C2 | semidirect |
| 2. D16×D181 | C2 | semidirect |
| 3. #26041116 | C2 | semidirect |
| 4. D5792 | C2 | semidirect |
| 5. #26041114 | C2 | semidirect |
| 6. #26041112 | C2 | semidirect |
| 7. SD64×C181 | C2 | semidirect |
| 12. D2896 | C22 | semidirect |
| 15. #19153722 | C22 | semidirect |
| 16. Q32×C181 | C22 | semidirect |
| 18. C32×C181 | C22 | semidirect |
| 54. C181 | #2263 | semidirect |
| 59. SD64 | D181 | semidirect |
| 65. Q32 | C2×D181 | semidirect |
| 73. C32 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041712 | 2 |
| D16×D181 | 2 |
| #26041116 | 2 |
| D5792 | 2 |
| #26041114 | 2 |
| #26041112 | 2 |
| SD64×C181 | 2 |
| #2263 | 181 |