Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626310 | C2 | semidirect |
| 2. D4×#11924031 | C2 | semidirect |
| 3. #22624954 | C2 | semidirect |
| 4. #22624882 | C2 | semidirect |
| 5. D4⋊#11924031 | C2 | semidirect |
| 6. #22624846 | C2 | semidirect |
| 52. #11924013 | C16 | semidirect |
| 74. D4×C73 | C2×C16 | semidirect |
| 83. D292 | C2×C16 | semidirect |
| 91. #10596831 | C2×C16 | semidirect |
| 121. C73 | #12062 | semidirect |
| 190. D4 | #14556664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626310 | 2 |
| D4×#11924031 | 2 |
| #22624954 | 2 |
| #22624882 | 2 |
| D4⋊#11924031 | 2 |
| #22624846 | 2 |
| #22608723 | 2 |
| #12062 | 73 |