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. C4×C7×D21 | C2 | semidirect |
| 3. C3×C7×Dic14 | C2 | semidirect |
| 4. #11924248 | C2 | semidirect |
| 5. #11924246 | C2 | semidirect |
| 14. C7×Dic14 | D3 | semidirect |
| 33. C4×D21 | D7 | semidirect |
| 35. C3×Dic14 | D7 | semidirect |
| 38. C3×C72 | #41 | semidirect |
| 66. Dic14 | D21 | semidirect |
| 67. C72 | #239 | semidirect |
| 95. C3×C7 | #1157 | semidirect |
| 96. C3×C7 | #1161 | semidirect |
| 117. C7 | #66673 | semidirect |
| 118. C7 | #66732 | semidirect |
| 127. C3 | #11716103 | 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 |
| C4×C7×D21 | 2 |
| C3×C7×Dic14 | 2 |
| #11924248 | 2 |
| #11924246 | 2 |
| #11716103 | 3 |
| #66732 | 7 |
| #66673 | 7 |