Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | C2×#41×C47 | C2 |
| hypercenter | C2×#41 | D47 |
| hypocenter | C47 | #547 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625352 | C2 | semidirect |
| 2. #13094022 | C2 | semidirect |
| 3. #13094007 | C2 | semidirect |
| 4. #13094005 | C2 | semidirect |
| 5. #13094003 | C2 | semidirect |
| 6. #13094000 | C2 | semidirect |
| 7. #13093996 | C2 | semidirect |
| 8. D4×Dic47 | C2 | semidirect |
| 9. C4×C22⋊D47 | C2 | semidirect |
| 10. C2×Dic47⋊C4 | C2 | semidirect |
| 11. C2×#41×C47 | C2 | semidirect |
| 42. D4×C47 | D4 | semidirect |
| 76. Dic47 | #41 | semidirect |
| 84. C47 | #547 | semidirect |
| 86. C2×#41 | D47 | semidirect |
| 129. D4 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625352 | 2 |
| #13094022 | 2 |
| #13094007 | 2 |
| #13094005 | 2 |
| #13094003 | 2 |
| #13094000 | 2 |
| #13093996 | 2 |
| D4×Dic47 | 2 |
| C4×C22⋊D47 | 2 |
| C2×Dic47⋊C4 | 2 |
| C2×#41×C47 | 2 |
| #547 | 47 |