Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1174 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 191 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. #22571136 | C2 | semidirect |
| 3. #22565414 | C2 | semidirect |
| 4. #22559180 | C2 | semidirect |
| 5. #22558705 | C2 | semidirect |
| 6. C67×#1461 | C2 | semidirect |
| 109. C2×Q8×C67 | SD16 | semidirect |
| 186. #1461 | D67 | semidirect |
| 187. C67 | #18402 | semidirect |
| 267. C2×Q8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573980 | 2 |
| #22571136 | 2 |
| #22565414 | 2 |
| #22559180 | 2 |
| #22558705 | 2 |
| C67×#1461 | 2 |
| #18402 | 67 |