Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 124 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. #22626778 | C2 | semidirect |
| 2. #22625230 | C2 | semidirect |
| 3. #22625230 | C2 | semidirect |
| 4. #22625171 | C2 | semidirect |
| 5. #22624771 | C2 | semidirect |
| 6. #22624757 | C2 | semidirect |
| 66. C2×D8×C73 | C8 | semidirect |
| 110. C2×D4×C73 | C2×C8 | semidirect |
| 116. C2×C8×C73 | C2×C8 | semidirect |
| 202. C73 | #9089 | semidirect |
| 228. C2×D8 | #10596833 | semidirect |
| 275. C2×D4 | C2×#10596833 | semidirect |
| 299. C2×C8 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626778 | 2 |
| #22625230 | 2 |
| #22625171 | 2 |
| #22624771 | 2 |
| #22624757 | 2 |
| C2×#17988699 | 2 |
| #9089 | 73 |