Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
942 conjugacy classes of subgroups; only the 600 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 600 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×#11763698 | C2 | direct (N × H) |
| 4. C22×#63216 | C4 | semidirect |
| 6. #11763698 | C22 | direct (N × H) |
| 21. C2×#63216 | C2×C4 | semidirect |
| 40. #63216 | C22×C4 | semidirect |
| 58. C22×C17 | #346 | semidirect |
| 74. C2×C17 | C2×#346 | semidirect |
| 90. C17 | C22×#346 | semidirect |
| 120. C22 | #11763698 | direct (N × H) |
| 128. C2 | C2×#11763698 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63216 | 2 |
| C2×#11763698 | 2 |
| C22×C8×Dic17 | 2 |
| C22×#346 | 17 |