Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #26042007 | C2 | semidirect |
| 3. #26041681 | C2 | semidirect |
| 4. #26041677 | C2 | semidirect |
| 5. #26041587 | C2 | semidirect |
| 7. #26041575 | C2 | semidirect |
| 11. C8×Q8×C181 | C2 | semidirect |
| 47. #15668438 | Q8 | semidirect |
| 114. C181 | #3381 | semidirect |
| 124. C8×Q8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042007 | 2 |
| #26041989 | 2 |
| #26041681 | 2 |
| #26041677 | 2 |
| #26041587 | 2 |
| #26041580 | 2 |
| #26041575 | 2 |
| #26041560 | 2 |
| C4×#15668438 | 2 |
| C8×Q8×C181 | 2 |
| #3381 | 181 |