Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. #22624887 | C2 | direct (N × H) |
| 45. C2×Q16×C73 | C8 | semidirect |
| 75. Q16×C73 | C2×C8 | semidirect |
| 120. C2×C73 | #1332 | semidirect |
| 128. C73 | C2×#1332 | semidirect |
| 147. C2×Q16 | #10596833 | semidirect |
| 183. Q16 | C2×#10596833 | semidirect |
| 243. C2 | #22624887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989473 | 2 |
| C2×#17989450 | 2 |
| #22624887 | 2 |
| C2×Q16×Dic73 | 2 |
| C2×#1332 | 73 |