Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #26041617 | C2 | semidirect |
| 3. #26041561 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. #26041486 | C2 | semidirect |
| 6. #26041481 | C2 | semidirect |
| 8. C4×#15668439 | C2 | semidirect |
| 9. C4×#15668436 | C2 | semidirect |
| 10. #26041332 | C2 | semidirect |
| 11. #533×C181 | C2 | semidirect |
| 136. C181 | #3107 | semidirect |
| 138. #533 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668449 | 2 |
| #26041617 | 2 |
| #26041561 | 2 |
| #26041556 | 2 |
| #26041486 | 2 |
| #26041481 | 2 |
| #26041439 | 2 |
| C4×#15668439 | 2 |
| C4×#15668436 | 2 |
| #26041332 | 2 |
| #533×C181 | 2 |
| #3107 | 181 |