Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #22626948 | C2 | semidirect |
| 4. C8×#11924040 | C2 | semidirect |
| 38. #11924040 | M16 | semidirect |
| 49. #11924011 | C16 | semidirect |
| 72. C8×C73 | C2×C16 | semidirect |
| 73. #10596831 | C2×C16 | semidirect |
| 95. C73 | C16×M16 | semidirect |
| 163. C8 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627130 | 2 |
| C4×#14556686 | 2 |
| #22626948 | 2 |
| C8×#11924040 | 2 |
| #22625129 | 2 |
| C16×M16 | 73 |