Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
258 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11924003 | C2 | semidirect |
| 2. #22611750 | C2 | semidirect |
| 4. #22608000 | C2 | semidirect |
| 5. #22607887 | C2 | semidirect |
| 6. C16×#10596831 | C2 | semidirect |
| 7. C73×D4⋊C16 | C2 | semidirect |
| 47. #11924013 | C16 | semidirect |
| 58. #11924003 | D8 | semidirect |
| 74. D4×C73 | C2×C16 | semidirect |
| 83. D292 | C2×C16 | semidirect |
| 93. #10596831 | C2×C16 | semidirect |
| 119. D4⋊C16 | D73 | semidirect |
| 121. C73 | C16×D8 | semidirect |
| 190. D4 | C16×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11924003 | 2 |
| #22611750 | 2 |
| C8×#11924013 | 2 |
| #22608000 | 2 |
| #22607887 | 2 |
| C16×#10596831 | 2 |
| C73×D4⋊C16 | 2 |
| C16×D8 | 73 |