Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 24. #15691876 | C8 | direct (N × H) |
| 57. C8×C199 | Q16 | semidirect |
| 71. C199 | C8×Q16 | semidirect |
| 129. C8 | #15691876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic398 | 2 |
| C4×#15691876 | 2 |
| #27163770 | 2 |
| Q8⋊(C199⋊C8) | 2 |
| #27163748 | 2 |
| C8×C199⋊C8 | 2 |
| C8×Q8×C199 | 2 |
| C8×Q16 | 199 |