Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26041583 | C2 | semidirect |
| 3. #26041576 | C2 | semidirect |
| 4. #26041571 | C2 | semidirect |
| 5. #26041556 | C2 | semidirect |
| 6. #26041322 | C2 | semidirect |
| 7. C2×#19153749 | C2 | semidirect |
| 8. #26041306 | C2 | semidirect |
| 11. #544×C181 | C2 | semidirect |
| 42. #15668449 | Q8 | semidirect |
| 123. C181 | #3083 | semidirect |
| 125. #544 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041759 | 2 |
| #26041583 | 2 |
| #26041576 | 2 |
| #26041571 | 2 |
| #26041556 | 2 |
| #26041322 | 2 |
| C2×#19153749 | 2 |
| #26041306 | 2 |
| #26041278 | 2 |
| #26041273 | 2 |
| #544×C181 | 2 |
| #3083 | 181 |