Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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, Fitting, socle, cosocle | C2×C3×C72 | C23 |
| hypocenter | C3×C72 | #41 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924253 | C2 | semidirect |
| 2. #11924250 | C2 | semidirect |
| 3. #11924247 | C2 | semidirect |
| 4. Dic3×C7⋊D7 | C2 | semidirect |
| 5. C7×D21⋊C4 | C2 | semidirect |
| 6. C7×Dic3×D7 | C2 | semidirect |
| 7. C3×#87641 | C2 | semidirect |
| 21. #87641 | D3 | semidirect |
| 46. D21⋊C4 | D7 | semidirect |
| 50. Dic3×D7 | D7 | semidirect |
| 51. C3×C72 | #41 | semidirect |
| 90. C72 | #237 | semidirect |
| 127. C3×C7 | #1157 | semidirect |
| 128. C3×C7 | #1157 | semidirect |
| 155. C7 | #66669 | semidirect |
| 156. C7 | #66683 | semidirect |
| 168. C3 | #11716102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924253 | 2 |
| #11924250 | 2 |
| #11924247 | 2 |
| Dic3×C7⋊D7 | 2 |
| C7×D21⋊C4 | 2 |
| C7×Dic3×D7 | 2 |
| C3×#87641 | 2 |
| #11716102 | 3 |
| #66683 | 7 |
| #66669 | 7 |