Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 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×#19153744 | C2 | semidirect |
| 3. C2×#19153743 | C2 | semidirect |
| 4. C2×#19153742 | C2 | semidirect |
| 5. M16×Dic181 | C2 | semidirect |
| 6. C4×#15668428 | C2 | semidirect |
| 7. C2×#104×C181 | C2 | semidirect |
| 10. #19153814 | C4 | semidirect |
| 11. #19153812 | C4 | semidirect |
| 12. #19153805 | C4 | semidirect |
| 13. #19153803 | C4 | semidirect |
| 45. #15668433 | D4 | semidirect |
| 71. M16×C181 | D4 | semidirect |
| 140. Dic181 | #104 | semidirect |
| 148. C181 | #1980 | semidirect |
| 154. C2×#104 | D181 | semidirect |
| 206. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041825 | 2 |
| C2×#19153744 | 2 |
| C2×#19153743 | 2 |
| C2×#19153742 | 2 |
| M16×Dic181 | 2 |
| C4×#15668428 | 2 |
| C2×#104×C181 | 2 |
| #1980 | 181 |