Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26041631 | C2 | semidirect |
| 3. #26041614 | C2 | semidirect |
| 4. #26041571 | C2 | semidirect |
| 5. #26041518 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 7. #26041434 | C2 | semidirect |
| 8. C4×#15668439 | C2 | semidirect |
| 10. C2×#19153739 | C2 | semidirect |
| 92. D4×C181 | Q16 | semidirect |
| 122. C181 | #3299 | semidirect |
| 208. D4 | #15668439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic362 | 2 |
| #26041631 | 2 |
| #26041614 | 2 |
| #26041571 | 2 |
| #26041518 | 2 |
| #26041489 | 2 |
| #26041434 | 2 |
| C4×#15668439 | 2 |
| D4×#13089678 | 2 |
| C2×#19153739 | 2 |
| #554×C181 | 2 |
| #3299 | 181 |