Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26041653 | C2 | semidirect |
| 3. D4×#13089678 | C2 | semidirect |
| 4. #26041029 | C2 | semidirect |
| 5. #26041025 | C2 | semidirect |
| 6. #26041022 | C2 | semidirect |
| 7. #474×C181 | C2 | semidirect |
| 52. #13089678 | D8 | semidirect |
| 57. D4×C181 | SD16 | semidirect |
| 85. C181 | #1665 | semidirect |
| 88. #474 | D181 | semidirect |
| 139. D4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041653 | 2 |
| #26041474 | 2 |
| D4×#13089678 | 2 |
| #26041029 | 2 |
| #26041025 | 2 |
| #26041022 | 2 |
| #474×C181 | 2 |
| #1665 | 181 |