Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
786 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 235 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. #14545931 | C2 | semidirect |
| 3. #14545927 | C2 | semidirect |
| 4. C4⋊C4×#3633 | C2 | semidirect |
| 6. C42×#3633 | C2 | semidirect |
| 41. C17×#126 | C8 | semidirect |
| 42. #10587584 | C8 | semidirect |
| 45. #10587565 | C8 | semidirect |
| 46. #10587562 | C8 | semidirect |
| 77. C4⋊C4×C17 | C2×C8 | semidirect |
| 79. C42×C17 | C2×C8 | semidirect |
| 83. C4⋊Dic17 | C2×C8 | semidirect |
| 84. #63225 | C2×C8 | semidirect |
| 85. #63225 | C2×C8 | semidirect |
| 86. C4×Dic17 | C2×C8 | semidirect |
| 107. #3633 | #126 | direct (N × H) |
| 170. #126 | #3633 | direct (N × H) |
| 188. C17 | C8×#126 | semidirect |
| 211. C4⋊C4 | C2×#3633 | semidirect |
| 223. C42 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545932 | 2 |
| #14545931 | 2 |
| #14545927 | 2 |
| C4⋊C4×#3633 | 2 |
| C22⋊C4×#3633 | 2 |
| C42×#3633 | 2 |
| #126×#595 | 2 |
| C8×#126 | 17 |