Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
162 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 82 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 | C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C4 | C23×C7 |
| prime radical | C2×C7×#41 | C2 |
| LCS | G ▷ 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. C2×C7×M16 | C2 | semidirect |
| 3. C2×C7×C4⋊C4 | C2 | semidirect |
| 4. C7×#103 | C2 | semidirect |
| 5. C7×#102 | C2 | semidirect |
| 7. C7×#41 | C4 | semidirect |
| 18. #417 | C7 | direct (N × H) |
| 22. C7×Q8 | C2×C4 | semidirect |
| 25. C7×D4 | C2×C4 | semidirect |
| 36. C2×M16 | C2×C7 | semidirect |
| 37. C2×C4⋊C4 | C2×C7 | semidirect |
| 38. #103 | C2×C7 | semidirect |
| 39. #102 | C2×C7 | semidirect |
| 53. #41 | C4×C7 | semidirect |
| 72. Q8 | C2×C4×C7 | semidirect |
| 75. D4 | C2×C4×C7 | semidirect |
| 85. C7 | #417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C2×C7×M16 | 2 |
| C2×C7×C4⋊C4 | 2 |
| C7×#103 | 2 |
| C7×#102 | 2 |
| #417 | 7 |