Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#19153745 | C2 | semidirect |
| 3. C2×#19153739 | C2 | semidirect |
| 5. #26041184 | C2 | semidirect |
| 7. #340×C181 | C2 | semidirect |
| 82. C2×Dic181 | SD16 | semidirect |
| 129. C181 | #2055 | semidirect |
| 137. #340 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668438 | 2 |
| C2×#19153745 | 2 |
| C2×#19153739 | 2 |
| C2×#19153736 | 2 |
| #26041184 | 2 |
| #26041180 | 2 |
| #340×C181 | 2 |
| #2055 | 181 |