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. D21⋊Dic3 | C2 | semidirect |
| 2. #92691 | C2 | semidirect |
| 3. #92688 | C2 | semidirect |
| 4. D3×C7×Dic3 | C2 | semidirect |
| 5. D7×C3⋊Dic3 | C2 | semidirect |
| 6. C3×#4246 | C2 | semidirect |
| 7. C3×#4245 | C2 | semidirect |
| 24. #4246 | D3 | semidirect |
| 26. #4245 | D3 | semidirect |
| 61. D3×Dic3 | D7 | semidirect |
| 62. C32×C7 | #41 | semidirect |
| 112. C3×C7 | #237 | semidirect |
| 113. C3×C7 | #237 | semidirect |
| 140. C32 | #1157 | semidirect |
| 148. C7 | #3805 | semidirect |
| 167. C3 | #66669 | semidirect |
| 168. C3 | #66683 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D21⋊Dic3 | 2 |
| #92691 | 2 |
| #92688 | 2 |
| D3×C7×Dic3 | 2 |
| D7×C3⋊Dic3 | 2 |
| C3×#4246 | 2 |
| C3×#4245 | 2 |
| #66683 | 3 |
| #66669 | 3 |
| #3805 | 7 |