Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
106 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 106 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, socle | C22×C7 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C7 |
| prime radical | C7×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#117 | C2 | semidirect |
| 3. C7×#107 | C2 | semidirect |
| 4. C7×#106 | C2 | semidirect |
| 5. C7×#102 | C2 | semidirect |
| 6. C7×#102 | C2 | semidirect |
| 7. C7×C22⋊C8 | C2 | semidirect |
| 19. #482 | C7 | direct (N × H) |
| 35. #117 | C2×C7 | semidirect |
| 36. #107 | C2×C7 | semidirect |
| 37. #106 | C2×C7 | semidirect |
| 38. #102 | C2×C7 | semidirect |
| 39. #102 | C2×C7 | semidirect |
| 40. C22⋊C8 | C2×C7 | semidirect |
| 84. C7 | #482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#121 | 2 |
| C7×#117 | 2 |
| C7×#107 | 2 |
| C7×#106 | 2 |
| C7×#102 | 2 |
| C7×C22⋊C8 | 2 |
| #482 | 7 |