Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #26041585 | C2 | semidirect |
| 4. #26041584 | C2 | semidirect |
| 5. #26041571 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 7. #26041564 | C2 | semidirect |
| 11. #477×C181 | C2 | semidirect |
| 47. Q8×D181 | Q8 | semidirect |
| 130. C181 | #3078 | semidirect |
| 137. #477 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×Q8×D181 | 2 |
| #26041585 | 2 |
| #26041584 | 2 |
| #26041571 | 2 |
| #26041565 | 2 |
| #26041564 | 2 |
| #26041320 | 2 |
| #26041301 | 2 |
| #26041286 | 2 |
| #477×C181 | 2 |
| #3078 | 181 |