Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C22⋊D47 |
| commutator, cosocle | C4×C47 | C24 |
| Frattini | C4 | C23×D47 |
| Fitting | 2−1+4×C47 | C2 |
| socle | C2×C47 | C22×D4 |
| hypercenter | 2−1+4 | D47 |
| hypocenter | C47 | #578 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094071 | C2 | semidirect |
| 2. #13094055 | C2 | semidirect |
| 3. #13094054 | C2 | semidirect |
| 4. #13094044 | C2 | semidirect |
| 5. C2×#10625337 | C2 | semidirect |
| 6. #13094031 | C2 | semidirect |
| 7. 2−1+4×C47 | C2 | semidirect |
| 53. C47 | #578 | semidirect |
| 55. 2−1+4 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094071 | 2 |
| #13094055 | 2 |
| #13094054 | 2 |
| #13094044 | 2 |
| C2×#10625337 | 2 |
| #13094031 | 2 |
| 2−1+4×C47 | 2 |
| #578 | 47 |