Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
350 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22562438 | C2 | semidirect |
| 3. #22562348 | C2 | semidirect |
| 4. #22558257 | C2 | semidirect |
| 5. #22558172 | C2 | semidirect |
| 65. Dic268 | SD16 | semidirect |
| 142. C67 | #12370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic268 | 2 |
| #22562438 | 2 |
| #22562348 | 2 |
| #22558257 | 2 |
| #22558172 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×#1673 | 2 |
| #12370 | 67 |