Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Dic94 | C2 | semidirect |
| 3. #13093989 | C2 | semidirect |
| 4. D4×Dic47 | C2 | semidirect |
| 5. C4×C22⋊D47 | C2 | semidirect |
| 6. (C22⋊D47)⋊C4 | C2 | semidirect |
| 7. #13093982 | C2 | semidirect |
| 8. #13093980 | C2 | semidirect |
| 9. C2×C4×Dic47 | C2 | semidirect |
| 10. C42×D47 | C2 | semidirect |
| 11. C4×D4×C47 | C2 | semidirect |
| 17. #10625352 | C4 | direct (N × H) |
| 38. D4×C47 | C2×C4 | semidirect |
| 44. C22⋊D47 | C2×C4 | semidirect |
| 46. C2×Dic47 | C2×C4 | semidirect |
| 54. C4×D47 | C2×C4 | semidirect |
| 55. Dic94 | C2×C4 | semidirect |
| 66. C4×C47 | #41 | semidirect |
| 71. Dic47 | #41 | semidirect |
| 78. C47 | C4×#41 | semidirect |
| 85. C4×D4 | D47 | semidirect |
| 118. D4 | C4×D47 | semidirect |
| 149. C4 | #10625352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625352 | 2 |
| C4×Dic94 | 2 |
| #13093989 | 2 |
| D4×Dic47 | 2 |
| C4×C22⋊D47 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| #13093982 | 2 |
| #13093980 | 2 |
| C2×C4×Dic47 | 2 |
| C42×D47 | 2 |
| C4×D4×C47 | 2 |
| C4×#41 | 47 |