Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. C2×Q8×D7 | C2 | semidirect |
| 3. C2×C7×SD16 | C2 | semidirect |
| 4. C2×#1144 | C2 | semidirect |
| 5. C2×#1142 | C2 | semidirect |
| 6. #6478 | C2 | direct (N × H) |
| 7. C2×Dic28 | C2 | semidirect |
| 8. C2×#1131 | C2 | semidirect |
| 14. Q8×D7 | C22 | semidirect |
| 22. C7×SD16 | C22 | semidirect |
| 24. #1144 | C22 | semidirect |
| 25. #1142 | C22 | semidirect |
| 27. Dic28 | C22 | semidirect |
| 28. #1131 | C22 | semidirect |
| 59. C2×SD16 | D7 | semidirect |
| 88. SD16 | C2×D7 | semidirect |
| 93. C2×C7 | #137 | semidirect |
| 119. C7 | C2×#137 | semidirect |
| 133. C2 | #6478 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D7 | 2 |
| C2×#1159 | 2 |
| C2×C7×SD16 | 2 |
| C2×#1144 | 2 |
| C2×#1142 | 2 |
| #6478 | 2 |
| C2×Dic28 | 2 |
| C2×#1131 | 2 |
| C2×#137 | 7 |