Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1766 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1766 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22588255 | C2 | semidirect |
| 5. C2×#14556043 | C22 | semidirect |
| 9. C23×D4×C71 | C4 | semidirect |
| 13. C2×#127×C71 | C4 | semidirect |
| 15. C22×C42×C71 | C4 | semidirect |
| 84. C2×D4×C71 | C22⋊C4 | semidirect |
| 96. C42×C71 | C22⋊C4 | semidirect |
| 163. C22×C71 | #353 | semidirect |
| 183. C71 | #12693 | semidirect |
| 185. C23×D4 | Dic71 | semidirect |
| 189. C2×#127 | Dic71 | semidirect |
| 191. C22×C42 | Dic71 | semidirect |
| 260. C2×D4 | C22⋊Dic71 | semidirect |
| 276. C42 | C22⋊Dic71 | semidirect |
| 343. C22 | #17985792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985792 | 2 |
| #22588255 | 2 |
| C22×#127×C71 | 2 |
| #12693 | 71 |