Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
336 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #22625070 | C2 | semidirect |
| 4. #22625064 | C2 | semidirect |
| 13. #17988979 | C4 | semidirect |
| 16. #17988944 | C4 | semidirect |
| 21. #17988648 | C4 | semidirect |
| 22. #541×C73 | C4 | semidirect |
| 47. #14556502 | C2×C4 | semidirect |
| 48. C4×#10596831 | C2×C4 | semidirect |
| 49. C4⋊Q8×C73 | C2×C4 | semidirect |
| 52. #125×C73 | C2×C4 | semidirect |
| 159. C73 | #13610 | semidirect |
| 160. #541 | #64408 | semidirect |
| 183. C4⋊Q8 | C2×#64408 | semidirect |
| 188. #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 |
| #22625064 | 2 |
| #22620997 | 2 |
| #13610 | 73 |