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. #11924255 | C2 | semidirect |
| 2. #11924249 | C2 | semidirect |
| 3. #11924239 | C2 | semidirect |
| 4. C7×Dic3×D7 | C2 | semidirect |
| 5. C3×#87640 | C2 | semidirect |
| 16. #87640 | D3 | semidirect |
| 33. Dic3×D7 | D7 | semidirect |
| 34. C3×C72 | #41 | semidirect |
| 57. C72 | #237 | semidirect |
| 81. C3×C7 | #1157 | semidirect |
| 100. C7 | #66683 | semidirect |
| 109. C3 | #11716102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924255 | 2 |
| #11924249 | 2 |
| #11924239 | 2 |
| C7×Dic3×D7 | 2 |
| C3×#87640 | 2 |
| #11716102 | 3 |
| #66683 | 7 |