Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 136 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 | #120 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C2×C29×2−1+4 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#104 | C2 | semidirect |
| 3. C29×#417 | C2 | semidirect |
| 4. C2×C29×#101 | C2 | semidirect |
| 5. C29×#391 | C2 | semidirect |
| 8. C29×2−1+4 | C4 | semidirect |
| 81. #1793 | C29 | direct (N × H) |
| 97. C2×#104 | C2×C29 | semidirect |
| 98. #417 | C2×C29 | semidirect |
| 99. C2×#101 | C2×C29 | semidirect |
| 100. #391 | C2×C29 | semidirect |
| 109. 2−1+4 | C4×C29 | semidirect |
| 123. C29 | #1793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×2−1+4 | 2 |
| C2×C29×#104 | 2 |
| C29×#417 | 2 |
| C2×C29×#101 | 2 |
| C29×#391 | 2 |
| #1793 | 29 |