Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D271 | C2 | semidirect |
| 3. #22576091 | C2 | semidirect |
| 4. #22576082 | C2 | semidirect |
| 5. #22576080 | C2 | semidirect |
| 6. (C2×D271)⋊C8 | C2 | semidirect |
| 7. #106×C271 | C2 | semidirect |
| 52. C271 | #481 | semidirect |
| 57. #106 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22576135 | 2 |
| C4⋊C4×D271 | 2 |
| #22576091 | 2 |
| #22576082 | 2 |
| #22576080 | 2 |
| (C2×D271)⋊C8 | 2 |
| #106×C271 | 2 |
| #481 | 271 |