Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D21 |
| commutator, socle, cosocle | C2×C32×C7 | C23 |
| Fitting | C22×C32×C7 | C22 |
| hypercenter | C22 | D3×D21 |
| hypocenter | C32×C7 | #41 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #92726 | C2 | semidirect |
| 2. C3×#4268 | C2 | semidirect |
| 3. C2×C3×C7×Dic3 | C2 | semidirect |
| 4. #92691 | C2 | semidirect |
| 5. #92689 | C2 | semidirect |
| 6. #92687 | C2 | semidirect |
| 7. Dic3×D21 | C2 | semidirect |
| 21. #4268 | D3 | semidirect |
| 26. C2×C7×Dic3 | D3 | semidirect |
| 57. C2×C3×Dic3 | D7 | semidirect |
| 62. C32×C7 | #41 | semidirect |
| 105. C2×Dic3 | D21 | semidirect |
| 113. C3×C7 | #235 | semidirect |
| 114. C3×C7 | #237 | semidirect |
| 141. C32 | #1157 | semidirect |
| 149. C7 | #3804 | semidirect |
| 169. C3 | #66683 | semidirect |
| 170. C3 | #66728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92726 | 2 |
| C3×#4268 | 2 |
| C2×C3×C7×Dic3 | 2 |
| #92691 | 2 |
| #92689 | 2 |
| #92687 | 2 |
| Dic3×D21 | 2 |
| #66728 | 3 |
| #66683 | 3 |
| #3804 | 7 |