Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C2×C7×D8 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×SD16 | C2 | semidirect |
| 3. C7×#124 | C2 | semidirect |
| 4. C4×C7×D4 | C2 | semidirect |
| 5. C7×C4⋊C8 | C2 | semidirect |
| 6. C7×#103 | C2 | semidirect |
| 7. C7×#102 | C2 | semidirect |
| 21. #463 | C7 | direct (N × H) |
| 38. C2×SD16 | C2×C7 | semidirect |
| 40. #124 | C2×C7 | semidirect |
| 41. C4×D4 | C2×C7 | semidirect |
| 42. C4⋊C8 | C2×C7 | semidirect |
| 43. #103 | C2×C7 | semidirect |
| 44. #102 | C2×C7 | semidirect |
| 92. C7 | #463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD16 | 2 |
| C2×C7×D8 | 2 |
| C7×#124 | 2 |
| C4×C7×D4 | 2 |
| C7×C4⋊C8 | 2 |
| C7×#103 | 2 |
| C7×#102 | 2 |
| #463 | 7 |