Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 297 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. D4×#11924040 | C2 | semidirect |
| 2. #22627128 | C2 | semidirect |
| 3. C2×C22⋊#11924040 | C2 | semidirect |
| 5. C22×#11924040 | C22 | semidirect |
| 6. C4⋊#11924040 | C22 | semidirect |
| 8. C22⋊#11924040 | C22 | semidirect |
| 9. C4×#11924040 | C22 | semidirect |
| 58. C2×D4×C73 | C16 | semidirect |
| 63. C23×C73 | C2×C16 | semidirect |
| 66. D4×C73 | C2×C16 | semidirect |
| 67. C2×C4×C73 | C2×C16 | semidirect |
| 108. C73 | #33486 | semidirect |
| 141. C2×D4 | #11924040 | semidirect |
| 167. C23 | C2×#11924040 | semidirect |
| 170. D4 | C2×#11924040 | semidirect |
| 182. C2×C4 | C2×#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11924040 | 2 |
| #22627128 | 2 |
| C2×C22⋊#11924040 | 2 |
| C2×D4×#10596833 | 2 |
| #33486 | 73 |