Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22571131 | C2 | semidirect |
| 2. #22565162 | C2 | semidirect |
| 3. #22558891 | C2 | semidirect |
| 4. #22558704 | C2 | semidirect |
| 5. #22558600 | C2 | semidirect |
| 6. #22558110 | C2 | semidirect |
| 110. C2×D4×C67 | SD16 | semidirect |
| 224. C67 | #10240 | semidirect |
| 313. C2×D4 | #11761616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571131 | 2 |
| #22565162 | 2 |
| #22558891 | 2 |
| #22558704 | 2 |
| #22558600 | 2 |
| #22558110 | 2 |
| C67×#3036 | 2 |
| #10240 | 67 |