Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
760 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22560526 | C2 | semidirect |
| 3. C2×#16863129 | C2 | semidirect |
| 4. #22558052 | C2 | semidirect |
| 5. C67×#1444 | C2 | semidirect |
| 55. #95×C67 | D4 | semidirect |
| 233. #1444 | D67 | semidirect |
| 235. C67 | #10402 | semidirect |
| 285. #95 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566311 | 2 |
| #22560526 | 2 |
| C2×#16863129 | 2 |
| #22558052 | 2 |
| C67×#1444 | 2 |
| #10402 | 67 |