Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
400 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 79 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⋊C16×D67 | C2 | semidirect |
| 3. #22560246 | C2 | semidirect |
| 4. #22558228 | C2 | semidirect |
| 5. #22558226 | C2 | semidirect |
| 6. #22558224 | C2 | semidirect |
| 7. C67×#1349 | C2 | semidirect |
| 185. #1349 | D67 | semidirect |
| 186. C67 | #11893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569788 | 2 |
| C22⋊C16×D67 | 2 |
| #22560246 | 2 |
| #22558228 | 2 |
| #22558226 | 2 |
| #22558224 | 2 |
| C67×#1349 | 2 |
| #11893 | 67 |