Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
348 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 56 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. #22626212 | C2 | semidirect |
| 2. #22626208 | C2 | semidirect |
| 3. #22625070 | C2 | semidirect |
| 4. #22625062 | C2 | semidirect |
| 13. #17988974 | C4 | semidirect |
| 16. #17988944 | C4 | semidirect |
| 21. #17988648 | C4 | semidirect |
| 22. #540×C73 | C4 | semidirect |
| 47. #14556502 | C2×C4 | semidirect |
| 48. C4×#10596831 | C2×C4 | semidirect |
| 49. #127×C73 | C2×C4 | semidirect |
| 50. #125×C73 | C2×C4 | semidirect |
| 165. C73 | #13609 | semidirect |
| 166. #540 | #64408 | semidirect |
| 191. #127 | C2×#64408 | semidirect |
| 192. #125 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626212 | 2 |
| #22626208 | 2 |
| #22625070 | 2 |
| #22625062 | 2 |
| #22620975 | 2 |
| #13609 | 73 |