Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
554 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 554 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. C22×#14523987 | C2 | semidirect |
| 3. #22570703 | C2 | semidirect |
| 4. C2×#16863211 | C2 | semidirect |
| 5. C2×#16863202 | C2 | semidirect |
| 6. #22558298 | C2 | semidirect |
| 7. C67×#1978 | C2 | semidirect |
| 206. #1978 | D67 | semidirect |
| 208. C67 | #13337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| C22×#14523987 | 2 |
| #22570703 | 2 |
| C2×#16863211 | 2 |
| C2×#16863202 | 2 |
| #22558298 | 2 |
| C67×#1978 | 2 |
| #13337 | 67 |