Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22562117 | C2 | semidirect |
| 3. #22559580 | C2 | semidirect |
| 5. #22558257 | C2 | semidirect |
| 7. C67×#1371 | C2 | semidirect |
| 70. C16×C67 | SD16 | semidirect |
| 114. #1371 | D67 | semidirect |
| 117. C67 | #12444 | semidirect |
| 180. C16 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562465 | 2 |
| #22562117 | 2 |
| #22559580 | 2 |
| #22559570 | 2 |
| #22558257 | 2 |
| #22558254 | 2 |
| C67×#1371 | 2 |
| #12444 | 67 |