Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×D72 |
| commutator, cosocle | C2×C72 | C23×C3 |
| Frattini | C2 | C2×C3×D72 |
| Fitting | C3×C4×C72 | C22 |
| socle | C2×C3×C72 | C23 |
| hypercenter | C3×C4 | D72 |
| hypocenter | C72 | C3×#41 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4⋊(C7⋊D7) | C2 | semidirect |
| 2. C3×C4×C7×D7 | C2 | semidirect |
| 3. C3×C7×Dic14 | C2 | semidirect |
| 4. C3×#87641 | C2 | semidirect |
| 5. C3×#87639 | C2 | semidirect |
| 6. #11716103 | C3 | direct (N × H) |
| 12. C4⋊(C7⋊D7) | C2×C3 | semidirect |
| 13. C4×C7×D7 | C2×C3 | semidirect |
| 14. C7×Dic14 | C2×C3 | semidirect |
| 15. #87641 | C2×C3 | semidirect |
| 16. #87639 | C2×C3 | semidirect |
| 36. C3×C4×D7 | D7 | semidirect |
| 37. C3×Dic14 | D7 | semidirect |
| 38. C3×C72 | #41 | semidirect |
| 65. C4×D7 | C3×D7 | semidirect |
| 66. Dic14 | C3×D7 | semidirect |
| 67. C72 | C3×#41 | semidirect |
| 95. C3×C7 | #1157 | semidirect |
| 96. C3×C7 | #1161 | semidirect |
| 117. C7 | C3×#1157 | semidirect |
| 118. C7 | C3×#1161 | semidirect |
| 127. C3 | #11716103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊(C7⋊D7) | 2 |
| C3×C4×C7×D7 | 2 |
| C3×C7×Dic14 | 2 |
| C3×#87641 | 2 |
| C3×#87639 | 2 |
| #11716103 | 3 |
| C3×#1161 | 7 |
| C3×#1157 | 7 |