Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
328 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26041005 | C2 | semidirect |
| 4. #26041004 | C2 | semidirect |
| 5. #324×C181 | C2 | semidirect |
| 30. C2×C4×D181 | C8 | semidirect |
| 55. C2×Dic181 | C2×C8 | semidirect |
| 69. C2×C4×C181 | C2×C8 | semidirect |
| 97. D181 | #324 | direct (N × H) |
| 98. C181 | C2×#324 | semidirect |
| 104. #324 | D181 | direct (N × H) |
| 167. C2×C4 | C8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D181 | 2 |
| C22⋊C8×D181 | 2 |
| #26041005 | 2 |
| #26041004 | 2 |
| #324×C181 | 2 |
| C2×#324 | 181 |