Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
414 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#11763731 | C2 | semidirect |
| 2. C2×C8×#3624 | C2 | semidirect |
| 3. #14543747 | C2 | direct (N × H) |
| 8. #11763731 | C22 | semidirect |
| 10. C8×#3624 | C22 | semidirect |
| 30. C2×Dic68 | C8 | semidirect |
| 33. #10587590 | C8 | semidirect |
| 35. C2×D136 | C8 | semidirect |
| 83. Dic68 | C2×C8 | semidirect |
| 85. D136 | C2×C8 | semidirect |
| 158. C2×C17 | #1335 | semidirect |
| 193. C17 | C2×#1335 | semidirect |
| 281. C2 | #14543747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763731 | 2 |
| C2×C8×#3624 | 2 |
| #14543747 | 2 |
| C2×#11762925 | 2 |
| C2×#1335 | 17 |