Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 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. #26041629 | C2 | semidirect |
| 3. #26041564 | C2 | semidirect |
| 5. Q8×#13089678 | C2 | semidirect |
| 7. #557×C181 | C2 | semidirect |
| 53. Q8×C181 | SD16 | semidirect |
| 74. C181 | #3359 | semidirect |
| 76. #557 | D181 | semidirect |
| 122. Q8 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D724 | 2 |
| #26041629 | 2 |
| #26041564 | 2 |
| #26041481 | 2 |
| Q8×#13089678 | 2 |
| C4×#15668436 | 2 |
| #557×C181 | 2 |
| #3359 | 181 |