Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 656 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×C37 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C2×#127×C37 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×SD16×C37 | C2 | semidirect |
| 2. C2×C4⋊Q8×C37 | C2 | semidirect |
| 4. C37×#492 | C2 | direct (N × H) |
| 5. C2×C4×C8×C37 | C2 | semidirect |
| 10. C2×SD16×C37 | C22 | semidirect |
| 13. C4⋊Q8×C37 | C22 | semidirect |
| 18. C4×C8×C37 | C22 | semidirect |
| 32. C2×C8×C37 | D4 | semidirect |
| 48. C2×C4×C37 | SD16 | semidirect |
| 53. C8×C37 | C2×D4 | semidirect |
| 62. C4×C37 | C2×SD16 | semidirect |
| 64. C2×#492 | C37 | direct (N × H) |
| 66. C2×C37 | #492 | direct (N × H) |
| 69. C22×SD16 | C2×C37 | semidirect |
| 70. C2×C4⋊Q8 | C2×C37 | semidirect |
| 72. #492 | C2×C37 | direct (N × H) |
| 73. C2×C4×C8 | C2×C37 | semidirect |
| 74. C37 | C2×#492 | direct (N × H) |
| 79. C2×SD16 | C22×C37 | semidirect |
| 82. C4⋊Q8 | C22×C37 | semidirect |
| 87. C4×C8 | C22×C37 | semidirect |
| 101. C2×C8 | D4×C37 | semidirect |
| 117. C2×C4 | SD16×C37 | semidirect |
| 122. C8 | C2×D4×C37 | semidirect |
| 131. C4 | C2×SD16×C37 | semidirect |
| 134. C2 | C37×#492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C37 | 2 |
| C2×C4⋊Q8×C37 | 2 |
| C2×#127×C37 | 2 |
| C37×#492 | 2 |
| C2×C4×C8×C37 | 2 |
| C2×#492 | 37 |