Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #22627052 | C2 | semidirect |
| 4. #22626934 | C2 | semidirect |
| 48. #14556580 | C8 | semidirect |
| 49. #14556579 | C8 | semidirect |
| 50. #14556578 | C8 | semidirect |
| 54. #124×C73 | C8 | semidirect |
| 79. C2×Dic146 | C2×C8 | semidirect |
| 93. C4×Dic73 | C2×C8 | semidirect |
| 94. C2×Q8×C73 | C2×C8 | semidirect |
| 97. C42×C73 | C2×C8 | semidirect |
| 176. C73 | #9099 | semidirect |
| 200. #124 | #10596842 | semidirect |
| 231. C2×Q8 | C2×#10596842 | semidirect |
| 268. C42 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627173 | 2 |
| #22627052 | 2 |
| #22627045 | 2 |
| #22626934 | 2 |
| #22626421 | 2 |
| #9099 | 73 |