Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
612 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626107 | C2 | semidirect |
| 3. #22625323 | C2 | semidirect |
| 5. #22624818 | C2 | semidirect |
| 6. #22624783 | C2 | semidirect |
| 25. #17988868 | C4 | semidirect |
| 26. #17988867 | C4 | semidirect |
| 27. #17988789 | C4 | semidirect |
| 32. #461×C73 | C4 | semidirect |
| 55. #14556591 | C2×C4 | semidirect |
| 72. C4⋊#10596831 | C2×C4 | semidirect |
| 79. C4⋊Q8×C73 | C2×C4 | semidirect |
| 81. C4⋊C8×C73 | C2×C4 | semidirect |
| 231. C73 | #9323 | semidirect |
| 239. #461 | #64408 | semidirect |
| 264. C4⋊Q8 | C2×#64408 | semidirect |
| 291. C4⋊C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626370 | 2 |
| #22626107 | 2 |
| #22625323 | 2 |
| #22625271 | 2 |
| #22624818 | 2 |
| #22624783 | 2 |
| #22620029 | 2 |
| #9323 | 73 |