Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
318 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 4. #22558262 | C2 | semidirect |
| 5. #22558261 | C2 | semidirect |
| 6. #22558260 | C2 | semidirect |
| 7. C67×#1363 | C2 | semidirect |
| 139. D67 | #1363 | direct (N × H) |
| 146. #1363 | D67 | direct (N × H) |
| 147. C67 | C2×#1363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D67 | 2 |
| C4⋊C16×D67 | 2 |
| #334×D67 | 2 |
| #22558262 | 2 |
| #22558261 | 2 |
| #22558260 | 2 |
| C67×#1363 | 2 |
| C2×#1363 | 67 |