Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
484 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 484 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. C4×#14556150 | C2 | semidirect |
| 3. #22590076 | C2 | semidirect |
| 4. #22590067 | C2 | semidirect |
| 5. #22586454 | C2 | semidirect |
| 6. #22586422 | C2 | semidirect |
| 7. C71×#1974 | 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 |
| 196. #1974 | D71 | semidirect |
| 199. C71 | #13027 | semidirect |
| 232. C2×Q16 | C4×D71 | semidirect |
| 236. 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 |
| C4×#14556150 | 2 |
| #22590076 | 2 |
| #22590067 | 2 |
| #22586454 | 2 |
| #22586422 | 2 |
| C71×#1974 | 2 |
| #13027 | 71 |