Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19153734 | C2 | semidirect |
| 3. C2×#19153733 | C2 | semidirect |
| 4. #26041242 | C2 | semidirect |
| 5. C2×#100×C181 | C2 | semidirect |
| 103. C181 | #1785 | semidirect |
| 108. C2×#100 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668448 | 2 |
| C2×#19153734 | 2 |
| C2×#19153733 | 2 |
| #26041242 | 2 |
| C2×#100×C181 | 2 |
| #1785 | 181 |