Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26041630 | C2 | semidirect |
| 4. #26041616 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041519 | C2 | semidirect |
| 7. #26041489 | C2 | semidirect |
| 8. #26041433 | C2 | semidirect |
| 10. #103×D181 | C2 | semidirect |
| 11. C4×Q16×C181 | C2 | semidirect |
| 81. D724 | Q16 | semidirect |
| 122. C181 | #3299 | semidirect |
| 132. C4×Q16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041989 | 2 |
| Q8×D724 | 2 |
| #26041630 | 2 |
| #26041616 | 2 |
| #26041574 | 2 |
| #26041519 | 2 |
| #26041489 | 2 |
| #26041433 | 2 |
| C8×D724 | 2 |
| #103×D181 | 2 |
| C4×Q16×C181 | 2 |
| #3299 | 181 |