Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×Dic134 | C2 | semidirect |
| 2. #22562433 | C2 | semidirect |
| 4. #22559570 | C2 | semidirect |
| 5. #22558265 | C2 | semidirect |
| 6. #22558189 | C2 | semidirect |
| 7. C67×#1331 | C2 | semidirect |
| 78. D8×C67 | SD16 | semidirect |
| 109. Dic134 | D16 | semidirect |
| 143. #1331 | D67 | semidirect |
| 144. C67 | #12352 | semidirect |
| 206. D8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic134 | 2 |
| #22562433 | 2 |
| #22562244 | 2 |
| #22559570 | 2 |
| #22558265 | 2 |
| #22558189 | 2 |
| C67×#1331 | 2 |
| #12352 | 67 |