Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22627128 | C2 | semidirect |
| 2. C2×C4×#11924040 | C2 | semidirect |
| 3. Q8⋊#11924040 | C2 | semidirect |
| 4. D4⋊#11924040 | C2 | semidirect |
| 86. #41×C73 | C16 | semidirect |
| 95. Q8×C73 | C2×C16 | semidirect |
| 98. D4×C73 | C2×C16 | semidirect |
| 152. C73 | #11613 | semidirect |
| 203. #41 | #11924040 | semidirect |
| 242. Q8 | C2×#11924040 | semidirect |
| 245. D4 | C2×#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627128 | 2 |
| C2×C4×#11924040 | 2 |
| Q8⋊#11924040 | 2 |
| D4⋊#11924040 | 2 |
| #41×#10596833 | 2 |
| #11613 | 73 |