Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22573311 | C2 | semidirect |
| 3. C2×#16863210 | C2 | semidirect |
| 4. C2×#16863208 | C2 | semidirect |
| 5. #22560256 | C2 | semidirect |
| 6. #22558325 | C2 | semidirect |
| 7. C67×#1389 | C2 | semidirect |
| 47. #14523983 | D4 | semidirect |
| 60. M32×C67 | D4 | semidirect |
| 175. #1389 | D67 | semidirect |
| 176. C67 | #13079 | semidirect |
| 222. M32 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573311 | 2 |
| #22569858 | 2 |
| C2×#16863210 | 2 |
| C2×#16863208 | 2 |
| #22560256 | 2 |
| #22558325 | 2 |
| C67×#1389 | 2 |
| #13079 | 67 |