Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
208 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D21⋊D7 |
| commutator, socle, cosocle | C2×C3×C72 | C23 |
| Frattini | C2 | C2×D21⋊D7 |
| Fitting | C3×C4×C72 | C22 |
| hypocenter | C3×C72 | #41 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C7×D21 | C2 | semidirect |
| 2. C3×C4×C7⋊D7 | C2 | semidirect |
| 3. #11924255 | C2 | semidirect |
| 4. #11924254 | C2 | semidirect |
| 5. #11924253 | C2 | semidirect |
| 12. C4×C7⋊D7 | D3 | semidirect |
| 26. C4×D21 | D7 | semidirect |
| 34. C3×C72 | #41 | semidirect |
| 57. C72 | #235 | semidirect |
| 81. C3×C7 | #1157 | semidirect |
| 100. C7 | #66675 | semidirect |
| 109. C3 | #11716102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D21 | 2 |
| C3×C4×C7⋊D7 | 2 |
| #11924255 | 2 |
| #11924254 | 2 |
| #11924253 | 2 |
| #11716102 | 3 |
| #66675 | 7 |