Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
208 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26041001 | C2 | semidirect |
| 5. #26041000 | C2 | semidirect |
| 6. #26041000 | C2 | semidirect |
| 7. #322×C181 | C2 | semidirect |
| 51. C8×C181 | M16 | semidirect |
| 66. C181 | #1451 | semidirect |
| 74. #322 | D181 | semidirect |
| 118. C8 | #15668432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041330 | 2 |
| C4×#15668432 | 2 |
| C4×C8×D181 | 2 |
| #26041001 | 2 |
| #26041000 | 2 |
| #322×C181 | 2 |
| #1451 | 181 |