Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
210 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 210 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 | C22⋊C4 |
| commutator | C22 | C22×C4×C7 |
| Frattini, cosocle | C23 | C23×C7 |
| prime radical | C22×C7×D4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C7×C22⋊C4 | C2 | semidirect |
| 3. C7×#99 | C2 | direct (N × H) |
| 4. C24×C7 | C4 | semidirect |
| 8. C2×C7×D4 | C4 | semidirect |
| 11. C22×C4×C7 | C4 | semidirect |
| 13. C7×C22⋊C4 | C22 | semidirect |
| 14. C2×#99 | C7 | direct (N × H) |
| 21. C23×C7 | C2×C4 | semidirect |
| 31. C2×C4×C7 | C2×C4 | semidirect |
| 33. C2×C22⋊C4 | C2×C7 | semidirect |
| 34. #99 | C2×C7 | direct (N × H) |
| 51. C24 | C4×C7 | semidirect |
| 55. C2×D4 | C4×C7 | semidirect |
| 58. C22×C4 | C4×C7 | semidirect |
| 60. C22⋊C4 | C22×C7 | semidirect |
| 66. C2×C7 | #99 | direct (N × H) |
| 74. C23 | C2×C4×C7 | semidirect |
| 84. C2×C4 | C2×C4×C7 | semidirect |
| 85. C7 | C2×#99 | direct (N × H) |
| 107. C2 | C7×#99 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D4 | 2 |
| C2×C7×C22⋊C4 | 2 |
| C7×#99 | 2 |
| C2×#99 | 7 |