Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
630 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 166 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 | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C24×C17 | C22⋊C4 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 3. C17×#1272 | C2 | semidirect |
| 18. C22×Q8×C17 | C8 | semidirect |
| 71. #7595 | C17 | direct (N × H) |
| 107. #1272 | C2×C17 | semidirect |
| 145. C22×Q8 | C8×C17 | semidirect |
| 162. C17 | #7595 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#391 | 2 |
| C17×#1817 | 2 |
| C17×#1272 | 2 |
| #7595 | 17 |