Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16863831 | C2 | semidirect |
| 2. C2×#16863666 | C2 | semidirect |
| 3. C2×#16863203 | C2 | semidirect |
| 4. C2×#16863196 | C2 | semidirect |
| 5. C2×#16863180 | C2 | semidirect |
| 6. #22558317 | C2 | semidirect |
| 7. C67×#3061 | C2 | semidirect |
| 40. C2×D536 | D4 | semidirect |
| 46. #14523983 | D4 | semidirect |
| 52. #14523979 | D4 | semidirect |
| 221. #3061 | D67 | semidirect |
| 226. C67 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863831 | 2 |
| C2×#16863666 | 2 |
| C2×#16863203 | 2 |
| C2×#16863196 | 2 |
| C2×#16863180 | 2 |
| #22558317 | 2 |
| C67×#3061 | 2 |
| #13307 | 67 |