Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
150 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 56. C8×C199 | Q16 | semidirect |
| 70. C199 | #1672 | semidirect |
| 127. C8 | #15691876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164416 | 2 |
| #27164313 | 2 |
| #27164228 | 2 |
| #27163769 | 2 |
| #27163766 | 2 |
| #27163763 | 2 |
| C8×Q8×C199 | 2 |
| #1672 | 199 |