Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. Q16×#10596833 | C2 | semidirect |
| 3. #22624964 | C2 | semidirect |
| 4. #22624887 | C2 | semidirect |
| 6. #22624845 | C2 | semidirect |
| 64. Q16×C73 | M16 | semidirect |
| 85. #10596833 | SD32 | semidirect |
| 113. C73 | #12071 | semidirect |
| 154. Q16 | #11924038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625563 | 2 |
| Q16×#10596833 | 2 |
| #22624964 | 2 |
| #22624887 | 2 |
| #22624886 | 2 |
| #22624845 | 2 |
| #22611780 | 2 |
| #12071 | 73 |