Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
408 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3245 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#1843 | C2 | semidirect |
| 3. C17×#1551 | C2 | semidirect |
| 4. C17×#1505 | C2 | semidirect |
| 5. C17×#1290 | C2 | semidirect |
| 66. #10512 | C17 | direct (N × H) |
| 92. #1843 | C2×C17 | semidirect |
| 93. #1551 | C2×C17 | semidirect |
| 94. #1505 | C2×C17 | semidirect |
| 95. #1290 | C2×C17 | semidirect |
| 150. C17 | #10512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#3245 | 2 |
| C17×#1843 | 2 |
| C17×#1551 | 2 |
| C17×#1505 | 2 |
| C17×#1290 | 2 |
| #10512 | 17 |