Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
644 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 106 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. #22626043 | C2 | semidirect |
| 4. #22626042 | C2 | semidirect |
| 5. #22624765 | C2 | semidirect |
| 6. #22624765 | C2 | semidirect |
| 25. #17988331 | C4 | semidirect |
| 26. #17988330 | C4 | semidirect |
| 27. #17988330 | C4 | semidirect |
| 28. #331×C73 | C4 | semidirect |
| 64. C4⋊#10596831 | C2×C4 | semidirect |
| 65. C4⋊#10596831 | C2×C4 | semidirect |
| 69. C4⋊C8×C73 | C2×C4 | semidirect |
| 70. C4⋊C8×C73 | C2×C4 | semidirect |
| 247. C73 | #8921 | semidirect |
| 268. #331 | #64408 | semidirect |
| 304. C4⋊C8 | C2×#64408 | semidirect |
| 305. C4⋊C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626461 | 2 |
| #22626059 | 2 |
| #22626043 | 2 |
| #22626042 | 2 |
| #22624765 | 2 |
| #331×D73 | 2 |
| #8921 | 73 |