Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 344 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. #22626354 | C2 | direct (N × H) |
| 2. C2×#17989519 | C2 | semidirect |
| 3. C22×#14556641 | C2 | semidirect |
| 5. #17989519 | C22 | semidirect |
| 8. C2×#14556641 | C22 | semidirect |
| 57. C2×C73 | #2258 | semidirect |
| 63. C73 | C2×#2258 | semidirect |
| 115. C2 | #22626354 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626354 | 2 |
| C2×#17989519 | 2 |
| C22×#14556641 | 2 |
| C2×#17989004 | 2 |
| C2×#2258 | 73 |