Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
190 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C23 |
| commutator | C22 | C22×C4×C7 |
| Frattini, cosocle | C23 | C23×C7 |
| prime radical | C24×C7 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×C4⋊C4 | C2 | semidirect |
| 5. C2×C42×C7 | C2 | semidirect |
| 6. C7×#95 | C2 | semidirect |
| 7. C7×#95 | C2 | semidirect |
| 18. C7×C22⋊C4 | C4 | semidirect |
| 20. #388 | C7 | direct (N × H) |
| 47. C2×C4⋊C4 | C2×C7 | semidirect |
| 51. C2×C42 | C2×C7 | semidirect |
| 52. #95 | C2×C7 | semidirect |
| 53. #95 | C2×C7 | semidirect |
| 84. C22⋊C4 | C4×C7 | semidirect |
| 120. C7 | #388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊C4 | 2 |
| C2×C7×C22⋊C4 | 2 |
| C2×C42×C7 | 2 |
| C7×#95 | 2 |
| #388 | 7 |