Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
446 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 128 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×C4⋊#11924031 | C2 | semidirect |
| 2. C2×#17989485 | C2 | semidirect |
| 3. C4×#14556665 | C2 | semidirect |
| 22. #14556665 | D4 | semidirect |
| 120. C4×C73 | #350 | semidirect |
| 134. C73 | #13193 | semidirect |
| 250. C4 | #17989485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11924031 | 2 |
| C2×#17989485 | 2 |
| C4×#14556665 | 2 |
| #22618643 | 2 |
| #13193 | 73 |