Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
874 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×D4×C17 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#1749 | C2 | semidirect |
| 3. C17×#1270 | C2 | semidirect |
| 13. C17×#336 | C22 | semidirect |
| 74. #7626 | C17 | direct (N × H) |
| 113. #1749 | C2×C17 | semidirect |
| 114. #1270 | C2×C17 | semidirect |
| 145. #336 | C22×C17 | semidirect |
| 175. C17 | #7626 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#390 | 2 |
| C17×#1749 | 2 |
| C17×#1270 | 2 |
| #7626 | 17 |