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. #22626095 | C2 | semidirect |
| 3. #22625320 | C2 | semidirect |
| 4. #22625271 | C2 | semidirect |
| 5. #22624818 | C2 | semidirect |
| 6. #22624783 | C2 | semidirect |
| 25. #17988878 | C4 | semidirect |
| 26. #17988877 | C4 | semidirect |
| 27. #17988779 | C4 | semidirect |
| 32. #459×C73 | C4 | semidirect |
| 57. #14556591 | C2×C4 | semidirect |
| 73. C4⋊#10596831 | C2×C4 | semidirect |
| 80. #127×C73 | C2×C4 | semidirect |
| 82. C4⋊C8×C73 | C2×C4 | semidirect |
| 166. D4×C73 | #104 | semidirect |
| 183. D292 | #104 | semidirect |
| 242. C73 | #9325 | semidirect |
| 250. #459 | #64408 | semidirect |
| 276. #127 | C2×#64408 | semidirect |
| 302. C4⋊C8 | C2×#64408 | semidirect |
| 397. D4 | #14556655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626370 | 2 |
| #22626095 | 2 |
| #22625320 | 2 |
| #22625271 | 2 |
| #22624818 | 2 |
| #22624783 | 2 |
| #22620021 | 2 |
| #9325 | 73 |