Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 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×#19153744 | C2 | semidirect |
| 3. #26041281 | C2 | semidirect |
| 4. #26041280 | C2 | semidirect |
| 5. C2×#19153734 | C2 | semidirect |
| 6. #26041185 | C2 | semidirect |
| 7. C2×#104×C181 | C2 | semidirect |
| 11. #19153863 | C4 | semidirect |
| 154. C181 | #1793 | semidirect |
| 158. C2×#104 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153863 | 2 |
| C2×#19153744 | 2 |
| #26041281 | 2 |
| #26041280 | 2 |
| C2×#19153734 | 2 |
| #26041185 | 2 |
| C2×#104×C181 | 2 |
| #1793 | 181 |