Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 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. #26041653 | C2 | semidirect |
| 3. #26041481 | C2 | semidirect |
| 4. #26041479 | C2 | semidirect |
| 5. Q8×#13089678 | C2 | semidirect |
| 6. C4×#15668436 | C2 | semidirect |
| 7. #557×C181 | C2 | semidirect |
| 52. #13089678 | #41 | semidirect |
| 55. Q8×C181 | SD16 | semidirect |
| 76. C181 | #3392 | semidirect |
| 78. #557 | D181 | semidirect |
| 124. Q8 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041951 | 2 |
| #26041653 | 2 |
| #26041481 | 2 |
| #26041479 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668436 | 2 |
| #557×C181 | 2 |
| #3392 | 181 |