Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 153 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 | direct (N × H) |
| 48. #11924012 | C16 | semidirect |
| 55. M16×C73 | C16 | semidirect |
| 74. C8×C73 | C2×C16 | semidirect |
| 75. #10596831 | C2×C16 | semidirect |
| 98. C73 | C16×M16 | semidirect |
| 133. M16 | #11924040 | direct (N × H) |
| 168. C8 | C2×#11924040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627128 | 2 |
| C2×C4×#11924040 | 2 |
| #22626948 | 2 |
| C8×#11924040 | 2 |
| M16×#10596833 | 2 |
| C16×M16 | 73 |