Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1470 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 549 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. #14545928 | C2 | direct (N × H) |
| 24. C2×C42×C17 | C8 | semidirect |
| 25. C2×C4×Dic17 | C8 | semidirect |
| 26. C42×D17 | C8 | semidirect |
| 48. C42×C17 | C2×C8 | semidirect |
| 49. C4×Dic17 | C2×C8 | semidirect |
| 65. C2×C4×C17 | C4⋊C8 | semidirect |
| 67. C2×Dic17 | C4⋊C8 | semidirect |
| 69. C4×D17 | C4⋊C8 | semidirect |
| 86. C4×C17 | C2×C4⋊C8 | semidirect |
| 87. Dic17 | C2×C4⋊C8 | semidirect |
| 96. C2×C17 | #1842 | semidirect |
| 98. D17 | #1842 | semidirect |
| 115. C2×C42 | #3633 | semidirect |
| 117. C17 | C2×#1842 | semidirect |
| 139. C42 | C2×#3633 | semidirect |
| 158. C2×C4 | C4⋊#3633 | semidirect |
| 173. C4 | C2×C4⋊#3633 | semidirect |
| 177. C2 | #14545928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#3633 | 2 |
| #14545928 | 2 |
| C2×C42×#595 | 2 |
| C2×#1842 | 17 |