Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
646 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 646 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. #22571127 | C2 | semidirect |
| 2. #22569675 | C2 | semidirect |
| 3. C2×#16863588 | C2 | semidirect |
| 4. #22558609 | C2 | semidirect |
| 5. #22558529 | C2 | semidirect |
| 6. #22558104 | C2 | semidirect |
| 7. C67×#1545 | C2 | semidirect |
| 93. C2×D268 | D8 | semidirect |
| 235. #1545 | D67 | semidirect |
| 239. C67 | #10176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571127 | 2 |
| #22569675 | 2 |
| C2×#16863588 | 2 |
| #22558609 | 2 |
| #22558529 | 2 |
| #22558104 | 2 |
| C67×#1545 | 2 |
| #10176 | 67 |