Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
614 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 144 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. C22⋊C4×#3624 | C2 | semidirect |
| 4. #14543627 | C2 | semidirect |
| 6. C22×#63242 | C4 | semidirect |
| 10. C2×#10587544 | C4 | semidirect |
| 11. C2×#10587543 | C4 | semidirect |
| 15. C2×C4×#3624 | C4 | semidirect |
| 17. #11763655 | C4 | semidirect |
| 18. #11763653 | C4 | semidirect |
| 56. #10587477 | C8 | semidirect |
| 96. C22⋊C4×C17 | C2×C8 | semidirect |
| 98. C22⋊Dic17 | C2×C8 | semidirect |
| 117. C22×D17 | C4×C8 | semidirect |
| 138. C2×Dic17 | C4×C8 | semidirect |
| 150. #3624 | #99 | semidirect |
| 241. C17 | C8×#99 | semidirect |
| 285. C22⋊C4 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763836 | 2 |
| C22⋊C4×#3624 | 2 |
| #14544022 | 2 |
| #14543627 | 2 |
| #14528571 | 2 |
| C8×#99 | 17 |