Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. #26042129 | C2 | semidirect |
| 4. Q8⋊#13089685 | C2 | semidirect |
| 30. Q8×D181 | C8 | semidirect |
| 57. Dic362 | C2×C8 | semidirect |
| 71. Q8×C181 | C2×C8 | semidirect |
| 96. D181 | Q8⋊C8 | semidirect |
| 97. C181 | C2×Q8⋊C8 | semidirect |
| 155. Q8 | D181⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D181⋊(C4⋊C8) | 2 |
| C4×D181⋊C8 | 2 |
| #26042129 | 2 |
| Q8⋊#13089685 | 2 |
| C4×Q8×D181 | 2 |
| C2×Q8⋊C8 | 181 |