Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22625512 | C2 | semidirect |
| 2. #22624964 | C2 | semidirect |
| 3. #22624886 | C2 | semidirect |
| 4. #22624842 | C2 | semidirect |
| 24. D1168 | C8 | semidirect |
| 38. D584 | C2×C8 | semidirect |
| 45. C16×C73 | C2×C8 | semidirect |
| 80. C73 | #12045 | semidirect |
| 120. C16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625512 | 2 |
| #22624964 | 2 |
| #22624886 | 2 |
| #22624842 | 2 |
| #22611777 | 2 |
| #12045 | 73 |