Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
160 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26041031 | C2 | semidirect |
| 6. #26041029 | C2 | semidirect |
| 7. #334×C181 | C2 | semidirect |
| 75. C181 | #1573 | semidirect |
| 83. #334 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041335 | 2 |
| #26041330 | 2 |
| C4⋊C8×D181 | 2 |
| #26041032 | 2 |
| #26041031 | 2 |
| #26041029 | 2 |
| #334×C181 | 2 |
| #1573 | 181 |