Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
252 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 88 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| prime radical | C29×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#432 | C2 | semidirect |
| 3. C29×#383 | C2 | semidirect |
| 4. C29×#327 | C2 | semidirect |
| 6. C29×C4⋊Q8 | C4 | semidirect |
| 7. C29×#127 | C4 | semidirect |
| 12. C4×D4×C29 | C4 | semidirect |
| 62. #1514 | C29 | direct (N × H) |
| 79. #432 | C2×C29 | semidirect |
| 80. #383 | C2×C29 | semidirect |
| 81. #327 | C2×C29 | semidirect |
| 88. C4⋊Q8 | C4×C29 | semidirect |
| 89. #127 | C4×C29 | semidirect |
| 94. C4×D4 | C4×C29 | semidirect |
| 102. C29 | #1514 | 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×#432 | 2 |
| C29×#383 | 2 |
| C29×#327 | 2 |
| #1514 | 29 |