Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4126 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2232 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×#10587542 | C2 | direct (N × H) |
| 4. C23×#3624 | C4 | semidirect |
| 6. C2×#10587542 | C22 | direct (N × H) |
| 20. C22×#3624 | C2×C4 | semidirect |
| 24. #10587542 | C23 | direct (N × H) |
| 37. C2×#3624 | C22×C4 | semidirect |
| 42. C23×C17 | #97 | semidirect |
| 55. #3624 | C23×C4 | semidirect |
| 59. C22×C17 | C2×#97 | semidirect |
| 76. C2×C17 | C22×#97 | semidirect |
| 93. C17 | C23×#97 | semidirect |
| 110. C23 | #10587542 | direct (N × H) |
| 124. C22 | C2×#10587542 | direct (N × H) |
| 133. C2 | C22×#10587542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#3624 | 2 |
| C22×#10587542 | 2 |
| C23×C4×Dic17 | 2 |
| C23×#97 | 17 |