Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1150 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 1. C2×#11763204 | C2 | semidirect |
| 2. C2×#11763168 | C2 | semidirect |
| 3. #14528090 | C2 | direct (N × H) |
| 4. C2×#11762549 | C2 | semidirect |
| 5. C2×#11762549 | C2 | semidirect |
| 9. C2×#10587555 | C22 | semidirect |
| 11. #11763204 | C22 | semidirect |
| 13. #11763168 | C22 | semidirect |
| 16. C2×#10587474 | C22 | semidirect |
| 17. C2×#10587474 | C22 | semidirect |
| 18. #11762549 | C22 | semidirect |
| 19. #11762549 | C22 | semidirect |
| 68. #10587555 | C23 | semidirect |
| 73. #10587474 | C23 | semidirect |
| 74. #10587474 | C23 | semidirect |
| 212. C2×C17 | #1659 | semidirect |
| 261. C17 | C2×#1659 | semidirect |
| 370. C2 | #14528090 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763204 | 2 |
| C2×#11763168 | 2 |
| #14528090 | 2 |
| C2×#11762549 | 2 |
| C2×C17×H(3,𝔽4) | 2 |
| C2×#1659 | 17 |