Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
616 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 1. #22627044 | C2 | semidirect |
| 2. #22626968 | C2 | semidirect |
| 3. #22626958 | C2 | semidirect |
| 41. #14556588 | C8 | semidirect |
| 43. #14556587 | C8 | semidirect |
| 44. #14556587 | C8 | semidirect |
| 46. #127×C73 | C8 | semidirect |
| 76. C2×D292 | C2×C8 | semidirect |
| 90. C4×Dic73 | C2×C8 | semidirect |
| 93. C2×D4×C73 | C2×C8 | semidirect |
| 94. C42×C73 | C2×C8 | semidirect |
| 186. C73 | #11475 | semidirect |
| 209. #127 | #10596842 | semidirect |
| 246. C2×D4 | C2×#10596842 | semidirect |
| 276. 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 |
| #22626968 | 2 |
| #22626958 | 2 |
| #127×#64408 | 2 |
| #11475 | 73 |