Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22571200 | C2 | semidirect |
| 2. #22571196 | C2 | semidirect |
| 3. #22558678 | C2 | semidirect |
| 4. #22558627 | C2 | semidirect |
| 5. #22558561 | C2 | semidirect |
| 6. #22558081 | C2 | semidirect |
| 7. C67×#3153 | C2 | semidirect |
| 215. #3153 | D67 | semidirect |
| 220. C67 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571200 | 2 |
| #22571196 | 2 |
| #22558678 | 2 |
| #22558627 | 2 |
| #22558561 | 2 |
| #22558081 | 2 |
| C67×#3153 | 2 |
| #10120 | 67 |