Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22570654 | C2 | semidirect |
| 2. #22570209 | C2 | semidirect |
| 3. #22561008 | C2 | semidirect |
| 4. #22558609 | C2 | semidirect |
| 5. #22558608 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 7. C67×#3100 | C2 | semidirect |
| 103. C2×C67⋊C8 | D8 | semidirect |
| 224. #3100 | D67 | semidirect |
| 229. C67 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570654 | 2 |
| #22570209 | 2 |
| #22561008 | 2 |
| #22558609 | 2 |
| #22558608 | 2 |
| #22558039 | 2 |
| C67×#3100 | 2 |
| #10032 | 67 |