Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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. C22×#15668439 | C2 | semidirect |
| 4. C2×#19153734 | C2 | semidirect |
| 6. #26041043 | C2 | semidirect |
| 7. C2×#101×C181 | C2 | semidirect |
| 122. C181 | #2020 | semidirect |
| 128. C2×#101 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| C2×#19153847 | 2 |
| C22×#15668439 | 2 |
| C2×#19153734 | 2 |
| #26041247 | 2 |
| #26041043 | 2 |
| C2×#101×C181 | 2 |
| #2020 | 181 |