Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
474 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 474 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 | C2×C37 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C37 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×M16×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C37×#3192 | C2 | semidirect |
| 2. C37×#2190 | C2 | semidirect |
| 3. C37×#2010 | C2 | semidirect |
| 4. C37×#1339 | C2 | semidirect |
| 5. C37×#1320 | C2 | semidirect |
| 6. C37×#575 | C22 | semidirect |
| 17. C37×#349 | C22 | semidirect |
| 18. C37×H(3,ℤ/4) | C22 | semidirect |
| 27. C2×D8×C37 | D4 | semidirect |
| 46. #106×C37 | D4 | semidirect |
| 134. #12114 | C37 | direct (N × H) |
| 156. #3192 | C2×C37 | semidirect |
| 157. #2190 | C2×C37 | semidirect |
| 158. #2010 | C2×C37 | semidirect |
| 159. #1339 | C2×C37 | semidirect |
| 160. #1320 | C2×C37 | semidirect |
| 167. #575 | C22×C37 | semidirect |
| 178. #349 | C22×C37 | semidirect |
| 179. H(3,ℤ/4) | C22×C37 | semidirect |
| 180. C37 | #12114 | direct (N × H) |
| 189. C2×D8 | D4×C37 | semidirect |
| 208. #106 | D4×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#3192 | 2 |
| C37×#2190 | 2 |
| C37×#2010 | 2 |
| C37×#1339 | 2 |
| C37×#1320 | 2 |
| #12114 | 37 |