Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
708 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22627072 | C2 | semidirect |
| 2. C2×(C2×#10596842)⋊C4 | C2 | semidirect |
| 3. #22626932 | C2 | semidirect |
| 4. #22626930 | C2 | semidirect |
| 49. C2×#11924029 | C8 | semidirect |
| 51. C2×#11924028 | C8 | semidirect |
| 53. C2×#11924027 | C8 | semidirect |
| 61. C2×#41×C73 | C8 | semidirect |
| 103. C2×Dic146 | C2×C8 | semidirect |
| 107. C2×D292 | C2×C8 | semidirect |
| 129. C2×Q8×C73 | C2×C8 | semidirect |
| 131. C2×D4×C73 | C2×C8 | semidirect |
| 262. C73 | #7578 | semidirect |
| 287. C2×#41 | #10596842 | semidirect |
| 331. C2×Q8 | C2×#10596842 | semidirect |
| 342. C2×D4 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627072 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| #22626932 | 2 |
| #22626930 | 2 |
| #22626392 | 2 |
| #7578 | 73 |