Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊Dic7 | C2 | semidirect |
| 3. #6408 | C2 | direct (N × H) |
| 4. C24×C7 | C4 | semidirect |
| 8. C2×C7×D4 | C4 | semidirect |
| 10. C22×C4×C7 | C4 | semidirect |
| 13. C22⋊Dic7 | C22 | semidirect |
| 21. C23×C7 | C2×C4 | semidirect |
| 29. C2×C4×C7 | C2×C4 | semidirect |
| 51. C24 | Dic7 | semidirect |
| 55. C2×D4 | Dic7 | semidirect |
| 58. C22×C4 | Dic7 | semidirect |
| 66. C2×C7 | #99 | semidirect |
| 74. C23 | C2×Dic7 | semidirect |
| 84. C2×C4 | C2×Dic7 | semidirect |
| 85. C7 | C2×#99 | semidirect |
| 107. C2 | #6408 | 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×C22⋊Dic7 | 2 |
| #6408 | 2 |
| C2×#99 | 7 |