Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22559033 | C2 | semidirect |
| 3. #22559032 | C2 | semidirect |
| 4. #22558274 | C2 | semidirect |
| 5. #22558177 | C2 | semidirect |
| 6. #22558131 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 27. #14523984 | C8 | semidirect |
| 47. D536 | C2×C8 | semidirect |
| 56. C67⋊C16 | C2×C8 | semidirect |
| 60. D8×C67 | C2×C8 | semidirect |
| 114. #1333 | D67 | semidirect |
| 116. C67 | #12067 | semidirect |
| 160. D8 | C8×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562083 | 2 |
| #22559033 | 2 |
| #22559032 | 2 |
| #22558274 | 2 |
| #22558177 | 2 |
| #22558131 | 2 |
| C67×#1333 | 2 |
| #12067 | 67 |