Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19153741 | C2 | semidirect |
| 3. C2×#19153738 | C2 | semidirect |
| 4. #26041139 | C2 | semidirect |
| 5. C2×C22⋊C8×C181 | C2 | semidirect |
| 9. C2×#15668449 | C4 | semidirect |
| 60. Dic362 | C22⋊C4 | semidirect |
| 63. D724 | C22⋊C4 | semidirect |
| 115. C181 | #1788 | semidirect |
| 120. C2×C22⋊C8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668449 | 2 |
| C2×#19153741 | 2 |
| C2×#19153738 | 2 |
| #26041139 | 2 |
| C2×C22⋊C8×C181 | 2 |
| #1788 | 181 |