Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #124×C47 | C2 |
| prime radical | #13093992 | C2 |
| hypercenter | #124 | D47 |
| hypocenter | C47 | #551 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094017 | C2 | semidirect |
| 2. #13094006 | C2 | semidirect |
| 3. #13094005 | C2 | semidirect |
| 4. #13094000 | C2 | semidirect |
| 6. (C22⋊D47)⋊C4 | C2 | semidirect |
| 7. #13093981 | C2 | semidirect |
| 8. C22⋊C4×D47 | C2 | semidirect |
| 9. #124×C47 | C2 | semidirect |
| 11. C2×Q8×C47 | C22 | semidirect |
| 14. C22×Dic47 | C22 | semidirect |
| 18. C22⋊C4×C47 | C22 | semidirect |
| 19. C42×C47 | C22 | semidirect |
| 22. C22⋊Dic47 | C22 | semidirect |
| 26. C4⋊Dic47 | C22 | semidirect |
| 27. Dic47⋊C4 | C22 | semidirect |
| 28. Dic47⋊C4 | C22 | semidirect |
| 29. Dic47⋊C4 | C22 | semidirect |
| 30. C4×Dic47 | C22 | semidirect |
| 69. C47 | #551 | semidirect |
| 71. #124 | D47 | semidirect |
| 80. C2×Q8 | C2×D47 | semidirect |
| 97. C22⋊C4 | C2×D47 | semidirect |
| 99. C42 | C2×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094017 | 2 |
| #13094006 | 2 |
| #13094005 | 2 |
| #13094000 | 2 |
| #13093992 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| #13093981 | 2 |
| C22⋊C4×D47 | 2 |
| #124×C47 | 2 |
| #551 | 47 |