Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22625363 | C2 | semidirect |
| 3. #22625315 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624786 | C2 | semidirect |
| 26. #17988878 | C4 | semidirect |
| 27. #17988877 | C4 | semidirect |
| 28. #17988864 | C4 | semidirect |
| 32. #474×C73 | C4 | semidirect |
| 55. #14556591 | C2×C4 | semidirect |
| 73. C4⋊#10596831 | C2×C4 | semidirect |
| 78. C4⋊Q8×C73 | C2×C4 | semidirect |
| 81. C4⋊C8×C73 | C2×C4 | semidirect |
| 233. C73 | #9175 | semidirect |
| 242. #474 | #64408 | semidirect |
| 264. C4⋊Q8 | C2×#64408 | semidirect |
| 295. C4⋊C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626444 | 2 |
| #22625363 | 2 |
| #22625315 | 2 |
| #22625231 | 2 |
| #22624827 | 2 |
| #22624786 | 2 |
| #22619723 | 2 |
| #9175 | 73 |