Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22560984 | C2 | semidirect |
| 3. #22558893 | C2 | semidirect |
| 5. C2×#16863144 | C2 | semidirect |
| 7. C67×#1283 | C2 | semidirect |
| 177. #1283 | D67 | semidirect |
| 178. C67 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570603 | 2 |
| #22560984 | 2 |
| #22558893 | 2 |
| #22558884 | 2 |
| C2×#16863144 | 2 |
| #22558609 | 2 |
| C67×#1283 | 2 |
| #10551 | 67 |