Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
502 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 502 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×Dic136 | C2 | semidirect |
| 3. C2×#11762648 | C2 | direct (N × H) |
| 4. C22×C17×C32 | C2 | semidirect |
| 8. C2×Dic136 | C22 | semidirect |
| 11. #11762648 | C22 | direct (N × H) |
| 13. C2×C17×C32 | C22 | semidirect |
| 24. Dic136 | C23 | semidirect |
| 27. C17×C32 | C23 | semidirect |
| 59. C22×C32 | D17 | semidirect |
| 60. C22×C17 | SD64 | semidirect |
| 75. C2×C32 | C2×D17 | semidirect |
| 76. C2×C17 | C2×SD64 | semidirect |
| 92. C32 | C22×D17 | semidirect |
| 93. C17 | C22×SD64 | semidirect |
| 123. C22 | #11762648 | direct (N × H) |
| 129. C2 | C2×#11762648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic136 | 2 |
| C22×D272 | 2 |
| C2×#11762648 | 2 |
| C22×C17×C32 | 2 |
| C22×SD64 | 17 |