Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 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, Frattini | C22 | C23×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | C22⋊Q8×C47 | C2 |
| prime radical | C2×C22⋊D47 | C22 |
| hypercenter | C22⋊Q8 | D47 |
| hypocenter | C47 | #554 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094023 | C2 | semidirect |
| 2. #13094014 | C2 | semidirect |
| 3. #13094004 | C2 | semidirect |
| 4. #13094001 | C2 | semidirect |
| 5. #13094000 | C2 | semidirect |
| 6. Q8×Dic47 | C2 | semidirect |
| 9. C2×C4⋊Dic47 | C2 | semidirect |
| 10. C4⋊C4×D47 | C2 | semidirect |
| 11. C22⋊Q8×C47 | C2 | semidirect |
| 43. C22⋊D47 | Q8 | semidirect |
| 75. C47 | #554 | semidirect |
| 81. C22⋊Q8 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094023 | 2 |
| #13094014 | 2 |
| #13094004 | 2 |
| #13094001 | 2 |
| #13094000 | 2 |
| Q8×Dic47 | 2 |
| C4×C22⋊D47 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| C2×C4⋊Dic47 | 2 |
| C4⋊C4×D47 | 2 |
| C22⋊Q8×C47 | 2 |
| #554 | 47 |