Finite Group DatabasebetaFinite Group DatabasebetaOrder 17344.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D271 |
| commutator, socle, cosocle | C22×C271 | C24 |
| Fitting | #117×C271 | C2 |
| hypercenter | #117 | D271 |
| hypocenter | C271 | #535 |
| LCS | G ▷ C22×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16864654 | C2 | semidirect |
| 2. C22×D1084 | C2 | semidirect |
| 3. #22576157 | C2 | semidirect |
| 4. #22576148 | C2 | semidirect |
| 5. #22576135 | C2 | semidirect |
| 6. #22576130 | C2 | semidirect |
| 7. #117×C271 | C2 | semidirect |
| 10. C2×Dic542 | C22 | semidirect |
| 14. C2×D1084 | C22 | semidirect |
| 15. C2×D1084 | C22 | semidirect |
| 17. C2×C4×D271 | C22 | semidirect |
| 18. (C2×D271)⋊C4 | C22 | semidirect |
| 20. C4⋊C4×C271 | C22 | semidirect |
| 22. C42×C271 | C22 | semidirect |
| 36. C2×C4×C271 | D4 | semidirect |
| 57. C271 | #535 | semidirect |
| 65. #117 | D271 | semidirect |
| 77. C4⋊C4 | C2×D271 | semidirect |
| 80. C42 | C2×D271 | semidirect |
| 94. C2×C4 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864654 | 2 |
| C22×D1084 | 2 |
| #22576157 | 2 |
| #22576148 | 2 |
| #22576135 | 2 |
| #22576130 | 2 |
| #117×C271 | 2 |
| #535 | 271 |