Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26042096 | C2 | semidirect |
| 2. #26041720 | C2 | semidirect |
| 3. #26041719 | C2 | semidirect |
| 4. #26041709 | C2 | semidirect |
| 5. C2×#19153762 | C2 | semidirect |
| 6. #26041696 | C2 | semidirect |
| 7. #578×C181 | C2 | semidirect |
| 73. C181 | #3417 | semidirect |
| 76. #578 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042096 | 2 |
| #26041720 | 2 |
| #26041719 | 2 |
| #26041709 | 2 |
| C2×#19153762 | 2 |
| #26041696 | 2 |
| #578×C181 | 2 |
| #3417 | 181 |