Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
460 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 216 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 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C29 |
| prime radical | C24×C29 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#484 | C2 | direct (N × H) |
| 4. C2×C29×#107 | C2 | semidirect |
| 5. C2×C29×#103 | C2 | semidirect |
| 20. C29×#107 | C22 | semidirect |
| 21. C29×#103 | C22 | semidirect |
| 68. C2×#484 | C29 | direct (N × H) |
| 85. #484 | C2×C29 | direct (N × H) |
| 86. C2×#107 | C2×C29 | semidirect |
| 87. C2×#103 | C2×C29 | semidirect |
| 90. C2×C29 | #484 | direct (N × H) |
| 107. #107 | C22×C29 | semidirect |
| 108. #103 | C22×C29 | semidirect |
| 110. C29 | C2×#484 | direct (N × H) |
| 171. C2 | C29×#484 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×C22⋊Q8 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C29×#484 | 2 |
| C2×C29×#107 | 2 |
| C2×C29×#103 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C2×#484 | 29 |