Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D72 |
| commutator, hypocenter | C3×C72 | C22×C4 |
| Fitting, socle, cosocle | C2×C3×C72 | C23 |
| prime radical | C2×C3×D72 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11924252 | C2 | semidirect |
| 3. D7×Dic21 | C2 | semidirect |
| 4. Dic3×C7⋊D7 | C2 | semidirect |
| 5. C7×Dic3×D7 | C2 | semidirect |
| 9. C3×D72 | C4 | semidirect |
| 10. C3⋊(C7⋊Dic7) | C22 | semidirect |
| 11. C7×Dic21 | C22 | semidirect |
| 12. C72×Dic3 | C22 | semidirect |
| 20. C3×C7⋊D7 | C2×C4 | semidirect |
| 21. C3×C7×D7 | C2×C4 | semidirect |
| 24. D72 | Dic3 | direct (N × H) |
| 35. Dic3×D7 | D7 | direct (N × H) |
| 36. C3×C72 | C22×C4 | semidirect |
| 39. C7⋊D7 | C2×Dic3 | semidirect |
| 40. C7×D7 | C2×Dic3 | semidirect |
| 48. Dic21 | C2×D7 | semidirect |
| 51. C7×Dic3 | C2×D7 | semidirect |
| 60. C72 | C22×Dic3 | semidirect |
| 67. C3×D7 | C4×D7 | semidirect |
| 85. C3×C7 | C2×C4×D7 | semidirect |
| 92. D7 | Dic3×D7 | direct (N × H) |
| 98. Dic3 | D72 | direct (N × H) |
| 105. C7 | C2×Dic3×D7 | semidirect |
| 115. C3 | C4×D72 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| #11924252 | 2 |
| D7×Dic21 | 2 |
| Dic3×C7⋊D7 | 2 |
| C7×Dic3×D7 | 2 |
| C4×D72 | 3 |
| C2×Dic3×D7 | 7 |