Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26041682 | C2 | semidirect |
| 3. #26041653 | C2 | semidirect |
| 4. #26041651 | C2 | semidirect |
| 5. #26041626 | C2 | semidirect |
| 6. C8×#13089678 | C2 | semidirect |
| 7. #486×C181 | C2 | semidirect |
| 46. #13089678 | D8 | semidirect |
| 47. #13089678 | SD16 | semidirect |
| 75. C181 | #1706 | semidirect |
| 82. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041682 | 2 |
| #26041655 | 2 |
| #26041653 | 2 |
| #26041651 | 2 |
| #26041626 | 2 |
| C8×#13089678 | 2 |
| #486×C181 | 2 |
| #1706 | 181 |