Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
366 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041977 | C2 | semidirect |
| 2. #26041680 | C2 | semidirect |
| 3. #26041606 | C2 | semidirect |
| 4. #26041597 | C2 | semidirect |
| 5. #26041582 | C2 | semidirect |
| 6. #26041516 | C2 | semidirect |
| 7. #26041515 | C2 | semidirect |
| 8. #26041361 | C2 | semidirect |
| 9. C8×C22⋊D181 | C2 | semidirect |
| 10. #26041316 | C2 | semidirect |
| 11. C2×#107×C181 | C2 | semidirect |
| 120. C181 | #3339 | semidirect |
| 132. C2×#107 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041977 | 2 |
| #26041680 | 2 |
| #26041606 | 2 |
| #26041597 | 2 |
| #26041582 | 2 |
| #26041516 | 2 |
| #26041515 | 2 |
| #26041361 | 2 |
| C8×C22⋊D181 | 2 |
| #26041316 | 2 |
| C2×#107×C181 | 2 |
| #3339 | 181 |