Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 176 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 | D32×D7 |
| commutator, Fitting, socle, cosocle | C2×C32×C7 | C23 |
| hypocenter | C32×C7 | #41 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #92695 | C2 | semidirect |
| 2. Dic3×D21 | C2 | semidirect |
| 3. C7×#627 | C2 | semidirect |
| 4. D7×C3⋊Dic3 | C2 | semidirect |
| 5. C3×#4246 | C2 | semidirect |
| 16. #4246 | D3 | semidirect |
| 37. #627 | D7 | semidirect |
| 40. C32×C7 | #41 | semidirect |
| 72. C3×C7 | #237 | semidirect |
| 90. C32 | #1161 | semidirect |
| 96. C7 | #3805 | semidirect |
| 109. C3 | #66670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92695 | 2 |
| Dic3×D21 | 2 |
| C7×#627 | 2 |
| D7×C3⋊Dic3 | 2 |
| C3×#4246 | 2 |
| #66670 | 3 |
| #3805 | 7 |