Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
782 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 320 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. C2×#11763735 | C2 | direct (N × H) |
| 7. #11763735 | C22 | direct (N × H) |
| 9. C22×#63214 | C4 | semidirect |
| 10. C2×C16×D17 | C4 | semidirect |
| 12. C22×C16×C17 | C4 | semidirect |
| 25. C2×C16×C17 | C2×C4 | semidirect |
| 26. C2×#63214 | C2×C4 | semidirect |
| 27. C16×D17 | C2×C4 | semidirect |
| 49. C16×C17 | C22×C4 | semidirect |
| 50. #63214 | C22×C4 | semidirect |
| 75. C22×C17 | #366 | semidirect |
| 77. C2×D17 | #366 | semidirect |
| 92. C22×C16 | #595 | semidirect |
| 96. C2×C17 | C2×#366 | semidirect |
| 98. D17 | C2×#366 | semidirect |
| 114. C2×C16 | C2×#595 | semidirect |
| 117. C17 | C22×#366 | semidirect |
| 139. C16 | C22×#595 | semidirect |
| 165. C22 | #11763735 | direct (N × H) |
| 175. C2 | C2×#11763735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587534 | 2 |
| C2×#11763735 | 2 |
| C22×C16×D17 | 2 |
| C22×#366 | 17 |