Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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. #26041631 | C2 | semidirect |
| 4. #26041583 | C2 | semidirect |
| 7. #26041489 | C2 | semidirect |
| 8. Q8×#13089678 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 11. #557×C181 | C2 | semidirect |
| 115. C181 | #3364 | semidirect |
| 117. #557 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041636 | 2 |
| #26041631 | 2 |
| #26041583 | 2 |
| #26041556 | 2 |
| #26041501 | 2 |
| #26041489 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668439 | 2 |
| C4×#15668436 | 2 |
| #557×C181 | 2 |
| #3364 | 181 |