Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
480 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22626967 | C2 | semidirect |
| 3. #22626959 | C2 | semidirect |
| 39. #14556580 | C8 | semidirect |
| 40. #14556579 | C8 | semidirect |
| 41. #14556578 | C8 | semidirect |
| 45. #124×C73 | C8 | semidirect |
| 70. C2×Dic146 | C2×C8 | semidirect |
| 84. C4×Dic73 | C2×C8 | semidirect |
| 85. C2×Q8×C73 | C2×C8 | semidirect |
| 88. C42×C73 | C2×C8 | semidirect |
| 165. C73 | #11477 | semidirect |
| 186. #124 | #10596842 | semidirect |
| 212. C2×Q8 | C2×#10596842 | semidirect |
| 249. C42 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627044 | 2 |
| #22626967 | 2 |
| #22626959 | 2 |
| #124×#64408 | 2 |
| #11477 | 73 |