Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
632 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626423 | C2 | semidirect |
| 2. #22626067 | C2 | semidirect |
| 3. #22625439 | C2 | semidirect |
| 4. #22625362 | C2 | semidirect |
| 5. #22624785 | C2 | semidirect |
| 6. #22624754 | C2 | semidirect |
| 22. #17988964 | C4 | semidirect |
| 23. #17988963 | C4 | semidirect |
| 24. #17988935 | C4 | semidirect |
| 28. #486×C73 | C4 | semidirect |
| 57. #14556588 | C2×C4 | semidirect |
| 70. C4×#10596831 | C2×C4 | semidirect |
| 71. C4⋊Q8×C73 | C2×C4 | semidirect |
| 74. C4×C8×C73 | C2×C4 | semidirect |
| 93. C4×#64408 | D8 | semidirect |
| 240. C73 | #9299 | semidirect |
| 247. #486 | #64408 | semidirect |
| 270. C4⋊Q8 | C2×#64408 | semidirect |
| 303. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626423 | 2 |
| #22626067 | 2 |
| #22625439 | 2 |
| #22625362 | 2 |
| #22624785 | 2 |
| #22624754 | 2 |
| #22620850 | 2 |
| #9299 | 73 |