Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7×D21 |
| commutator, socle, cosocle | C2×C3×C72 | C23 |
| Fitting | C3×C4×C72 | C22 |
| hypercenter | C4 | D7×D21 |
| hypocenter | C3×C72 | #41 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C3⋊(C7⋊D7) | C2 | semidirect |
| 2. C7×Dic42 | C2 | semidirect |
| 3. C3×C7×D28 | C2 | semidirect |
| 4. #11924249 | C2 | semidirect |
| 5. D7×Dic21 | C2 | semidirect |
| 13. C7×D28 | D3 | semidirect |
| 33. Dic42 | D7 | semidirect |
| 35. C3×D28 | D7 | semidirect |
| 38. C3×C72 | #41 | semidirect |
| 62. D28 | D21 | semidirect |
| 68. C72 | #237 | semidirect |
| 97. C3×C7 | #1159 | semidirect |
| 98. C3×C7 | #1161 | semidirect |
| 119. C7 | #66670 | semidirect |
| 120. C7 | #66730 | semidirect |
| 129. C3 | #11716100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊(C7⋊D7) | 2 |
| C7×Dic42 | 2 |
| C3×C7×D28 | 2 |
| #11924249 | 2 |
| D7×Dic21 | 2 |
| #11716100 | 3 |
| #66730 | 7 |
| #66670 | 7 |