Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22569149 | C2 | semidirect |
| 5. #22558774 | C2 | semidirect |
| 6. #22558068 | C2 | semidirect |
| 7. C67×#1275 | C2 | semidirect |
| 10. #16863769 | C4 | semidirect |
| 11. #16863743 | C4 | semidirect |
| 106. C2×C8×C67 | SD16 | semidirect |
| 183. #1275 | D67 | semidirect |
| 184. C67 | #9294 | semidirect |
| 273. C2×C8 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571152 | 2 |
| #22569149 | 2 |
| #22561033 | 2 |
| #22558876 | 2 |
| #22558774 | 2 |
| #22558068 | 2 |
| C67×#1275 | 2 |
| #9294 | 67 |