Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 65 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. D8×#10596842 | C2 | semidirect |
| 2. #22626998 | C2 | semidirect |
| 3. #22626977 | C2 | semidirect |
| 4. #22626946 | C2 | semidirect |
| 28. D1168 | C8 | semidirect |
| 29. #14556532 | C8 | semidirect |
| 31. D16×C73 | C8 | semidirect |
| 44. D584 | C2×C8 | semidirect |
| 47. #11924003 | C2×C8 | semidirect |
| 48. D8×C73 | C2×C8 | semidirect |
| 49. C16×C73 | C2×C8 | semidirect |
| 87. C73 | #12045 | semidirect |
| 103. D16 | #10596842 | semidirect |
| 118. D8 | C2×#10596842 | semidirect |
| 131. C16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#10596842 | 2 |
| #22626998 | 2 |
| #22626977 | 2 |
| #22626946 | 2 |
| D16×#64408 | 2 |
| #12045 | 73 |