Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 193 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 |
|---|---|---|
| 40. #101×C89 | C8 | semidirect |
| 89. #10623494 | #101 | direct (N × H) |
| 113. C89 | C8×#101 | semidirect |
| 142. #101 | #10623494 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10623494 | 2 |
| #26018576 | 2 |
| M16×#10623494 | 2 |
| #26018103 | 2 |
| C4×#101×C89 | 2 |
| C8×#101 | 89 |