Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
236 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C37 | C2×D4 |
| commutator | C2×C4 | C22×C8×C37 |
| Frattini, cosocle | C4×C8 | C23×C37 |
| socle | C22×C37 | C8×D4 |
| prime radical | C2×D8×C37 | C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C37 ◁ C4×C16×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#2169 | C2 | semidirect |
| 3. C37×#1367 | C2 | semidirect |
| 4. C37×D4⋊C16 | C2 | semidirect |
| 5. C37×#1312 | C2 | semidirect |
| 60. C8×C37 | M32 | semidirect |
| 62. #12064 | C37 | direct (N × H) |
| 73. #2169 | C2×C37 | semidirect |
| 75. #1367 | C2×C37 | semidirect |
| 76. D4⋊C16 | C2×C37 | semidirect |
| 77. #1312 | C2×C37 | semidirect |
| 92. C37 | #12064 | direct (N × H) |
| 137. C8 | M32×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2169 | 2 |
| C8×D8×C37 | 2 |
| C37×#1367 | 2 |
| C37×D4⋊C16 | 2 |
| C37×#1312 | 2 |
| #12064 | 37 |