Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
196 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×#13089678 | C2 | semidirect |
| 3. #26041344 | C2 | semidirect |
| 4. #26041031 | C2 | semidirect |
| 5. #26041008 | C2 | semidirect |
| 6. C8×#13089678 | C2 | semidirect |
| 7. D4⋊C8×C181 | C2 | semidirect |
| 25. #15668434 | C8 | semidirect |
| 44. D724 | C2×C8 | semidirect |
| 51. #13089678 | C2×C8 | semidirect |
| 52. #13089678 | D8 | semidirect |
| 55. D4×C181 | C2×C8 | semidirect |
| 83. C181 | C8×D8 | semidirect |
| 90. D4⋊C8 | D181 | semidirect |
| 131. D4 | C8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668434 | 2 |
| D4×#13089678 | 2 |
| #26041344 | 2 |
| #26041031 | 2 |
| #26041008 | 2 |
| C8×#13089678 | 2 |
| D4⋊C8×C181 | 2 |
| C8×D8 | 181 |