Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
520 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 264 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 | C24 |
| commutator | C22 | C23×C4×C29 |
| Frattini, cosocle | C23 | C24×C29 |
| prime radical | C22×D4×C29 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#391 | C2 | semidirect |
| 3. C29×#388 | C2 | semidirect |
| 5. C29×#385 | C2 | semidirect |
| 6. C29×#382 | C2 | semidirect |
| 10. C29×#124 | C4 | semidirect |
| 25. C2×Q8×C29 | C2×C4 | semidirect |
| 41. C22⋊C4×C29 | C2×C4 | semidirect |
| 43. C42×C29 | C2×C4 | semidirect |
| 68. #2379 | C29 | direct (N × H) |
| 85. #391 | C2×C29 | semidirect |
| 86. #388 | C2×C29 | semidirect |
| 88. #385 | C2×C29 | semidirect |
| 89. #382 | C2×C29 | semidirect |
| 99. #124 | C4×C29 | semidirect |
| 111. C29 | #2379 | direct (N × H) |
| 115. C2×Q8 | C2×C4×C29 | semidirect |
| 131. C22⋊C4 | C2×C4×C29 | semidirect |
| 133. C42 | C2×C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#124 | 2 |
| C29×#391 | 2 |
| C29×#388 | 2 |
| C29×#386 | 2 |
| C29×#385 | 2 |
| C29×#382 | 2 |
| #2379 | 29 |