Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
676 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 154 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×C29 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C2×C29×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2582 | C2 | semidirect |
| 4. C2×C29×Q8⋊C8 | C2 | semidirect |
| 5. C29×#1296 | C2 | semidirect |
| 55. C2×Q8×C29 | SD16 | semidirect |
| 91. #10230 | C29 | direct (N × H) |
| 129. #2582 | C2×C29 | semidirect |
| 131. C2×Q8⋊C8 | C2×C29 | semidirect |
| 132. #1296 | C2×C29 | semidirect |
| 201. C29 | #10230 | direct (N × H) |
| 208. C2×Q8 | SD16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#460 | 2 |
| C29×#2582 | 2 |
| C29×#1957 | 2 |
| C2×C29×Q8⋊C8 | 2 |
| C29×#1296 | 2 |
| #10230 | 29 |