Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
430 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C37 |
| prime radical | C22×D4×C37 | D4 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×#2099 | C2 | semidirect |
| 3. C37×#2072 | C2 | semidirect |
| 5. C37×#1272 | C2 | semidirect |
| 6. C37×#1271 | C2 | semidirect |
| 157. #7787 | C37 | direct (N × H) |
| 185. #2099 | C2×C37 | semidirect |
| 186. #2072 | C2×C37 | semidirect |
| 188. #1272 | C2×C37 | semidirect |
| 189. #1271 | C2×C37 | semidirect |
| 218. C37 | #7787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2732 | 2 |
| C37×#2099 | 2 |
| C37×#2072 | 2 |
| C37×#2071 | 2 |
| C37×#1272 | 2 |
| C37×#1271 | 2 |
| C37×#1270 | 2 |
| #7787 | 37 |