Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D272 | C2 | semidirect |
| 2. C2×#11762644 | C2 | direct (N × H) |
| 3. C22×#10587465 | C2 | semidirect |
| 4. C22×C17×D16 | C2 | semidirect |
| 7. C2×D272 | C22 | semidirect |
| 8. #11762644 | C22 | direct (N × H) |
| 9. C2×#10587465 | C22 | semidirect |
| 12. C2×C17×D16 | C22 | semidirect |
| 22. C17×D16 | C23 | semidirect |
| 26. D272 | C23 | semidirect |
| 27. #10587465 | C23 | semidirect |
| 58. C22×D16 | D17 | semidirect |
| 63. C22×C17 | D32 | semidirect |
| 74. C2×D16 | C2×D17 | semidirect |
| 79. C2×C17 | C2×D32 | semidirect |
| 92. D16 | C22×D17 | semidirect |
| 96. C17 | C22×D32 | semidirect |
| 129. C22 | #11762644 | direct (N × H) |
| 135. C2 | C2×#11762644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| C2×#11762644 | 2 |
| C22×#10587465 | 2 |
| C22×C17×D16 | 2 |
| C22×D32 | 17 |