Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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, Frattini, cosocle | C42 | C23×C29 |
| prime radical | C29×H(3,𝔽4) | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#497 | C2 | semidirect |
| 3. C29×#489 | C2 | semidirect |
| 4. C29×#329 | C2 | semidirect |
| 5. C29×#329 | C2 | semidirect |
| 8. C29×C4⋊Q8 | C22 | semidirect |
| 17. C29×#97 | C22 | semidirect |
| 18. C29×#97 | C22 | semidirect |
| 58. #1659 | C29 | direct (N × H) |
| 72. #497 | C2×C29 | semidirect |
| 73. #489 | C2×C29 | semidirect |
| 74. #329 | C2×C29 | semidirect |
| 75. #329 | C2×C29 | semidirect |
| 82. C4⋊Q8 | C22×C29 | semidirect |
| 91. #97 | C22×C29 | semidirect |
| 92. #97 | C22×C29 | semidirect |
| 93. C29 | #1659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×H(3,𝔽4) | 2 |
| C29×#497 | 2 |
| C29×#489 | 2 |
| C29×#329 | 2 |
| #1659 | 29 |