Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
196 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1402 |
| commutator | #127 | C2×C4×C17 |
| Frattini, cosocle | #492 | C22×C17 |
| prime radical | D42×C17 | C4 |
| LCS | G ▷ #127 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C42×C17 ◁ C17×#492 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#1410 | C2 | semidirect |
| 3. C17×#1359 | C2 | semidirect |
| 44. #7517 | C17 | direct (N × H) |
| 67. #1410 | C2×C17 | semidirect |
| 68. #1359 | C2×C17 | semidirect |
| 106. C17 | #7517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#1629 | 2 |
| C17×#1410 | 2 |
| C17×#1359 | 2 |
| #7517 | 17 |