Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16863207 | C2 | semidirect |
| 3. C2×#16863206 | C2 | semidirect |
| 4. #22561919 | C2 | semidirect |
| 5. #22560950 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 7. C67×#2139 | C2 | semidirect |
| 59. #14523975 | D4 | semidirect |
| 218. #2139 | D67 | semidirect |
| 221. C67 | #13410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570652 | 2 |
| C2×#16863207 | 2 |
| C2×#16863206 | 2 |
| #22561919 | 2 |
| #22560950 | 2 |
| #22558292 | 2 |
| C67×#2139 | 2 |
| #13410 | 67 |