Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 118 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. C4×#14556664 | C2 | semidirect |
| 2. #22625476 | C2 | semidirect |
| 3. #22624886 | C2 | semidirect |
| 4. #22624885 | C2 | semidirect |
| 8. #17989473 | C22 | semidirect |
| 11. #17989450 | C22 | semidirect |
| 33. D8×D73 | C8 | semidirect |
| 75. D584 | C2×C8 | semidirect |
| 93. D8×C73 | C2×C8 | semidirect |
| 163. D73 | #1331 | semidirect |
| 169. C73 | C2×#1331 | semidirect |
| 241. D8 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556664 | 2 |
| #22625476 | 2 |
| #22624886 | 2 |
| #22624885 | 2 |
| C4×D8×D73 | 2 |
| C2×#1331 | 73 |