Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
166 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #26041031 | C2 | semidirect |
| 5. #26041030 | C2 | semidirect |
| 6. #26041029 | C2 | semidirect |
| 7. #335×C181 | C2 | semidirect |
| 53. #13089678 | M16 | semidirect |
| 60. C8×C181 | M16 | semidirect |
| 77. C181 | #1569 | semidirect |
| 83. #335 | D181 | semidirect |
| 138. C8 | #15668432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041335 | 2 |
| #26041301 | 2 |
| C4×#15668432 | 2 |
| #26041031 | 2 |
| #26041030 | 2 |
| #26041029 | 2 |
| #335×C181 | 2 |
| #1569 | 181 |