Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
648 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | #99 |
| commutator | C22×C4 | C22×C4×C37 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C37 |
| socle | C22×C37 | C2×#99 |
| prime radical | C37×#2388 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C22×C4×C37 ◁ C2×C4×D4×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#99×C37 | C2 | semidirect |
| 3. C37×#1460 | C2 | semidirect |
| 4. C37×#1351 | C2 | semidirect |
| 5. C37×#1343 | C2 | semidirect |
| 6. C22×#41×C37 | C4 | semidirect |
| 11. C37×#395 | C4 | semidirect |
| 13. C37×#394 | C4 | semidirect |
| 19. C4×C22⋊C4×C37 | C4 | semidirect |
| 170. #11725 | C37 | direct (N × H) |
| 204. C4×#99 | C2×C37 | semidirect |
| 205. #1460 | C2×C37 | semidirect |
| 206. #1351 | C2×C37 | semidirect |
| 207. #1343 | C2×C37 | semidirect |
| 216. C22×#41 | C4×C37 | semidirect |
| 221. #395 | C4×C37 | semidirect |
| 223. #394 | C4×C37 | semidirect |
| 229. C4×C22⋊C4 | C4×C37 | semidirect |
| 233. C37 | #11725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#2388 | 2 |
| C4×#99×C37 | 2 |
| C37×#1460 | 2 |
| C37×#1351 | 2 |
| C37×#1343 | 2 |
| #11725 | 37 |