Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
768 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 206 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 |
| prime radical | C22×D8×C37 | C22 |
| 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. C37×#2658 | C2 | semidirect |
| 2. C37×#2644 | C2 | semidirect |
| 3. C37×#2043 | C2 | semidirect |
| 4. C37×#2042 | C2 | semidirect |
| 5. C37×#2013 | C2 | semidirect |
| 7. C37×#1840 | C2 | semidirect |
| 119. #32804 | C37 | direct (N × H) |
| 135. #2658 | C2×C37 | semidirect |
| 136. #2644 | C2×C37 | semidirect |
| 137. #2043 | C2×C37 | semidirect |
| 138. #2042 | C2×C37 | semidirect |
| 139. #2013 | C2×C37 | semidirect |
| 141. #1840 | C2×C37 | semidirect |
| 164. C37 | #32804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2658 | 2 |
| C37×#2644 | 2 |
| C37×#2043 | 2 |
| C37×#2042 | 2 |
| C37×#2013 | 2 |
| C37×#2012 | 2 |
| C37×#1840 | 2 |
| #32804 | 37 |