Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
398 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 398 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×C29 | #353 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | C4⋊Q8 | C23×C29 |
| prime radical | C23×C29 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C29 ◁ C22×C4×C29 ◁ C2×C29×C4⋊Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1411 | C2 | direct (N × H) |
| 65. C2×#1411 | C29 | direct (N × H) |
| 90. #1411 | C2×C29 | direct (N × H) |
| 114. C2×C29 | #1411 | direct (N × H) |
| 138. C29 | C2×#1411 | direct (N × H) |
| 203. C2 | C29×#1411 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#494 | 2 |
| C2×C29×#356 | 2 |
| C29×#1411 | 2 |
| C2×#1411 | 29 |