Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
594 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22561045 | C2 | semidirect |
| 3. #22560234 | C2 | semidirect |
| 4. #22558778 | C2 | semidirect |
| 5. C67×#1752 | C2 | semidirect |
| 6. C22×D536 | C4 | semidirect |
| 12. C2×#14523977 | C4 | semidirect |
| 14. C2×#14523965 | C4 | semidirect |
| 146. C8×C67 | #99 | semidirect |
| 181. #1752 | D67 | semidirect |
| 183. C67 | #9785 | semidirect |
| 324. C8 | #14523957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863632 | 2 |
| #22561045 | 2 |
| #22560234 | 2 |
| #22558778 | 2 |
| C67×#1752 | 2 |
| #9785 | 67 |