Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 372 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. #22561828 | C2 | semidirect |
| 3. #22560258 | C2 | semidirect |
| 4. #22558204 | C2 | semidirect |
| 5. #22558202 | C2 | semidirect |
| 6. #22558200 | C2 | semidirect |
| 7. C67×#1341 | C2 | semidirect |
| 188. #1341 | D67 | semidirect |
| 189. C67 | #11872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569869 | 2 |
| #22561828 | 2 |
| #22560258 | 2 |
| #22558204 | 2 |
| #22558202 | 2 |
| #22558200 | 2 |
| C67×#1341 | 2 |
| #11872 | 67 |