Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
488 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 488 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. #22569350 | C2 | semidirect |
| 3. #22561008 | C2 | semidirect |
| 4. #22558798 | C2 | semidirect |
| 5. #22558107 | C2 | semidirect |
| 6. #22558060 | C2 | semidirect |
| 7. C67×#1490 | C2 | semidirect |
| 232. #1490 | D67 | semidirect |
| 235. C67 | #9052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570256 | 2 |
| #22569350 | 2 |
| #22561008 | 2 |
| #22558798 | 2 |
| #22558107 | 2 |
| #22558060 | 2 |
| C67×#1490 | 2 |
| #9052 | 67 |