Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22562012 | C2 | semidirect |
| 3. #22558217 | C2 | semidirect |
| 4. C4×#106×C67 | C2 | semidirect |
| 6. #16863801 | C4 | semidirect |
| 7. #16863773 | C4 | semidirect |
| 12. C4×D536 | C4 | semidirect |
| 128. C4×#106 | D67 | semidirect |
| 130. C67 | #11744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570788 | 2 |
| #22562012 | 2 |
| #22558217 | 2 |
| C4×#106×C67 | 2 |
| #11744 | 67 |