Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22597225 | C2 | semidirect |
| 3. #22590075 | C2 | semidirect |
| 4. C2×#17985809 | C2 | semidirect |
| 5. #22586445 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#1976 | C2 | semidirect |
| 10. #17986440 | C4 | semidirect |
| 12. #17986435 | C4 | semidirect |
| 50. #14556068 | C2×C4 | semidirect |
| 62. C2×Q16×C71 | C2×C4 | semidirect |
| 64. C2×D8×C71 | C2×C4 | semidirect |
| 194. #1976 | D71 | semidirect |
| 197. C71 | #13030 | semidirect |
| 230. C2×Q16 | C4×D71 | semidirect |
| 234. C2×D8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22597225 | 2 |
| #22590075 | 2 |
| C2×#17985809 | 2 |
| #22586445 | 2 |
| #22586426 | 2 |
| C71×#1976 | 2 |
| #13030 | 71 |