Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26041032 | C2 | semidirect |
| 5. #26041028 | C2 | semidirect |
| 6. #26041025 | C2 | semidirect |
| 7. #498×C181 | C2 | semidirect |
| 59. C8×C181 | SD16 | semidirect |
| 76. C181 | #1691 | semidirect |
| 78. #498 | D181 | semidirect |
| 136. C8 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041566 | 2 |
| #26041481 | 2 |
| #26041358 | 2 |
| #26041032 | 2 |
| #26041028 | 2 |
| #26041025 | 2 |
| #498×C181 | 2 |
| #1691 | 181 |