Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
406 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. #14543740 | C2 | direct (N × H) |
| 24. C2×Q16×C17 | C8 | semidirect |
| 61. Q16×C17 | C2×C8 | semidirect |
| 139. C2×C17 | #1332 | semidirect |
| 146. C2×Q16 | #3624 | semidirect |
| 171. C17 | C2×#1332 | semidirect |
| 183. Q16 | C2×#3624 | semidirect |
| 243. C2 | #14543740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763695 | 2 |
| C2×#11763672 | 2 |
| #14543740 | 2 |
| C2×Q16×Dic17 | 2 |
| C2×#1332 | 17 |