Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
1102 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 270 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 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C37 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C37×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C37×#459 | C2 | semidirect |
| 2. C37×#2328 | C2 | semidirect |
| 3. C37×#2054 | C2 | semidirect |
| 4. C37×#1843 | C2 | semidirect |
| 5. C37×#1804 | C2 | semidirect |
| 25. #127×C37 | D4 | semidirect |
| 87. #28259 | C37 | direct (N × H) |
| 102. C2×#459 | C2×C37 | semidirect |
| 103. #2328 | C2×C37 | semidirect |
| 104. #2054 | C2×C37 | semidirect |
| 105. #1843 | C2×C37 | semidirect |
| 106. #1804 | C2×C37 | semidirect |
| 123. C37 | #28259 | direct (N × H) |
| 131. #127 | D4×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C37×#459 | 2 |
| C37×#2328 | 2 |
| C37×#2054 | 2 |
| C37×#1843 | 2 |
| C37×#1804 | 2 |
| #28259 | 37 |