Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
564 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14546026 | C2 | semidirect |
| 2. #14545904 | C2 | semidirect |
| 3. #14545904 | C2 | semidirect |
| 4. #14545898 | C2 | semidirect |
| 5. #14545794 | C2 | semidirect |
| 6. #14545788 | C2 | semidirect |
| 59. C2×D8×C17 | C8 | semidirect |
| 60. C2×#63228 | C8 | semidirect |
| 61. C2×#63228 | C8 | semidirect |
| 64. C2×D136 | C8 | semidirect |
| 89. C2×D4×C17 | C2×C8 | semidirect |
| 101. C2×D68 | C2×C8 | semidirect |
| 119. C2×C8×C17 | C2×C8 | semidirect |
| 122. C2×#3622 | C2×C8 | semidirect |
| 252. C2×D8 | #3633 | semidirect |
| 287. C17 | #9089 | semidirect |
| 303. C2×D4 | C2×#3633 | semidirect |
| 330. C2×C8 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546026 | 2 |
| #14545904 | 2 |
| #14545898 | 2 |
| #14545794 | 2 |
| #14545788 | 2 |
| C2×#11763850 | 2 |
| #9089 | 17 |