Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #99 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×D4 | C23×C29 |
| socle | C2×C29 | C2×#99 |
| prime radical | C29×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C4×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#410 | C2 | semidirect |
| 3. C29×#354 | C2 | semidirect |
| 4. C29×#353 | C2 | semidirect |
| 5. C2×#41×C29 | C4 | semidirect |
| 7. C29×C4⋊Q8 | C4 | semidirect |
| 9. C29×#124 | C4 | semidirect |
| 14. C2×C42×C29 | C4 | semidirect |
| 65. #2126 | C29 | direct (N × H) |
| 82. #410 | C2×C29 | semidirect |
| 83. #354 | C2×C29 | semidirect |
| 84. #353 | C2×C29 | semidirect |
| 90. C2×#41 | C4×C29 | semidirect |
| 92. C4⋊Q8 | C4×C29 | semidirect |
| 94. #124 | C4×C29 | semidirect |
| 99. C2×C42 | C4×C29 | semidirect |
| 102. C29 | #2126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#532 | 2 |
| C29×#410 | 2 |
| C29×#354 | 2 |
| C29×#353 | 2 |
| #2126 | 29 |