Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1154 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 203 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. #22570236 | C2 | semidirect |
| 2. #22565571 | C2 | semidirect |
| 3. #22559246 | C2 | semidirect |
| 4. #22559178 | C2 | semidirect |
| 5. #22558769 | C2 | semidirect |
| 6. #22558533 | C2 | semidirect |
| 105. C2×Q8×C67 | SD16 | semidirect |
| 202. C67 | #18219 | semidirect |
| 289. C2×Q8 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570236 | 2 |
| #22565571 | 2 |
| #22559246 | 2 |
| #22559178 | 2 |
| #22558769 | 2 |
| #22558533 | 2 |
| C67×#3497 | 2 |
| #18219 | 67 |