Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
434 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 70 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×C37 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C4⋊C4 | C23×C37 |
| prime radical | C37×#1598 | C2 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C23×C37 ◁ C2×C4⋊C4×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#2832 | C2 | semidirect |
| 2. C37×#2007 | C2 | semidirect |
| 3. C37×#1604 | C2 | semidirect |
| 5. C37×#1354 | C2 | semidirect |
| 6. C37×#1345 | C2 | semidirect |
| 7. C37×#1319 | C2 | semidirect |
| 168. #12199 | C37 | direct (N × H) |
| 194. #2832 | C2×C37 | semidirect |
| 195. #2007 | C2×C37 | semidirect |
| 196. #1604 | C2×C37 | semidirect |
| 198. #1354 | C2×C37 | semidirect |
| 199. #1345 | C2×C37 | semidirect |
| 200. #1319 | C2×C37 | semidirect |
| 227. C37 | #12199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2832 | 2 |
| C37×#2007 | 2 |
| C37×#1604 | 2 |
| C37×#1598 | 2 |
| C37×#1354 | 2 |
| C37×#1345 | 2 |
| C37×#1319 | 2 |
| #12199 | 37 |