Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
318 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 1. #22562466 | C2 | semidirect |
| 2. #22562433 | C2 | semidirect |
| 3. #22562432 | C2 | semidirect |
| 5. #22559803 | C2 | semidirect |
| 6. #22558128 | C2 | semidirect |
| 7. C67×#2248 | C2 | semidirect |
| 94. C67⋊C8 | SD32 | semidirect |
| 115. #2248 | D67 | semidirect |
| 121. C67 | #12529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562466 | 2 |
| #22562433 | 2 |
| #22562432 | 2 |
| #22559823 | 2 |
| #22559803 | 2 |
| #22558128 | 2 |
| C67×#2248 | 2 |
| #12529 | 67 |