Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#19153824 | C2 | semidirect |
| 3. #26041853 | C2 | semidirect |
| 4. #26041534 | C2 | semidirect |
| 5. #26041522 | C2 | semidirect |
| 6. #26041517 | C2 | semidirect |
| 7. #26041505 | C2 | semidirect |
| 8. #26041321 | C2 | semidirect |
| 9. #26041275 | C2 | semidirect |
| 10. C2×#19153740 | C2 | semidirect |
| 11. C2×#137×C181 | C2 | semidirect |
| 83. M16×C181 | D4 | semidirect |
| 143. C181 | #3063 | semidirect |
| 145. C2×#137 | D181 | semidirect |
| 210. M16 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153824 | 2 |
| #26041857 | 2 |
| #26041853 | 2 |
| #26041534 | 2 |
| #26041522 | 2 |
| #26041517 | 2 |
| #26041505 | 2 |
| #26041321 | 2 |
| #26041275 | 2 |
| C2×#19153740 | 2 |
| C2×#137×C181 | 2 |
| #3063 | 181 |