Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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. #14534744 | C2 | direct (N × H) |
| 2. C2×#11762738 | C2 | semidirect |
| 3. C2×#11762733 | C2 | semidirect |
| 5. C2×#11762707 | C2 | semidirect |
| 6. C2×C17×#376 | C2 | semidirect |
| 12. #11762738 | C22 | semidirect |
| 13. #11762733 | C22 | semidirect |
| 15. #11762707 | C22 | semidirect |
| 18. C17×#376 | C22 | semidirect |
| 98. C2×#376 | D17 | semidirect |
| 123. #376 | C2×D17 | semidirect |
| 127. C2×C17 | #2644 | semidirect |
| 152. C17 | C2×#2644 | semidirect |
| 219. C2 | #14534744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14534744 | 2 |
| C2×#11762738 | 2 |
| C2×#11762733 | 2 |
| C2×#11762711 | 2 |
| C2×#11762707 | 2 |
| C2×C17×#376 | 2 |
| C2×#2644 | 17 |