Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
650 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 650 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 |
|---|---|---|
| 1. #22626370 | C2 | semidirect |
| 2. #22626094 | C2 | semidirect |
| 3. #22625322 | C2 | semidirect |
| 4. #22625271 | C2 | semidirect |
| 5. #22624818 | C2 | semidirect |
| 6. #22624783 | C2 | semidirect |
| 25. #17988874 | C4 | semidirect |
| 26. #17988783 | C4 | semidirect |
| 27. #17988782 | C4 | semidirect |
| 32. #476×C73 | C4 | semidirect |
| 58. #14556588 | C2×C4 | semidirect |
| 73. C4⋊#10596831 | C2×C4 | semidirect |
| 79. C4⋊Q8×C73 | C2×C4 | semidirect |
| 82. C4⋊C8×C73 | C2×C4 | semidirect |
| 163. D4×C73 | #104 | semidirect |
| 183. D292 | #104 | semidirect |
| 242. C73 | #9325 | semidirect |
| 248. #476 | #64408 | semidirect |
| 275. C4⋊Q8 | C2×#64408 | semidirect |
| 302. C4⋊C8 | C2×#64408 | semidirect |
| 397. D4 | #14556656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626370 | 2 |
| #22626094 | 2 |
| #22625322 | 2 |
| #22625271 | 2 |
| #22624818 | 2 |
| #22624783 | 2 |
| #22620024 | 2 |
| #9325 | 73 |