Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22610874 | C2 | semidirect |
| 4. C4×#14556524 | C2 | semidirect |
| 5. #22608431 | C2 | semidirect |
| 6. #22608221 | C2 | semidirect |
| 9. #17988983 | C4 | semidirect |
| 10. #17988959 | C4 | semidirect |
| 11. #17988939 | C4 | semidirect |
| 12. #17988933 | C4 | semidirect |
| 163. #10596831 | #104 | semidirect |
| 198. C73 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620486 | 2 |
| #22610874 | 2 |
| #22610851 | 2 |
| C4×#14556524 | 2 |
| #22608431 | 2 |
| #22608221 | 2 |
| C73×#1502 | 2 |
| #9722 | 73 |