Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
550 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#17985792 | C2 | semidirect |
| 2. #22587054 | C2 | semidirect |
| 3. #22586485 | C2 | semidirect |
| 8. #17985792 | C22 | semidirect |
| 10. #17985743 | C22 | semidirect |
| 11. C2×H(5,𝔽2)×C71 | C4 | semidirect |
| 16. #453×C71 | C4 | semidirect |
| 19. C2×#100×C71 | C4 | semidirect |
| 29. H(5,𝔽2)×C71 | C2×C4 | semidirect |
| 52. #100×C71 | C2×C4 | semidirect |
| 196. C71 | #13561 | semidirect |
| 197. C2×H(5,𝔽2) | Dic71 | semidirect |
| 202. #453 | Dic71 | semidirect |
| 206. C2×#100 | Dic71 | semidirect |
| 215. H(5,𝔽2) | C2×Dic71 | semidirect |
| 240. #100 | C2×Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985792 | 2 |
| #22587054 | 2 |
| #22586485 | 2 |
| C2×#453×C71 | 2 |
| #13561 | 71 |