Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22626690 | C2 | semidirect |
| 2. #22626252 | C2 | semidirect |
| 3. #22626240 | C2 | semidirect |
| 4. #22626088 | C2 | semidirect |
| 5. #22624999 | C2 | semidirect |
| 6. #22624980 | C2 | semidirect |
| 24. C2×#14556536 | C4 | semidirect |
| 25. C2×#14556535 | C4 | semidirect |
| 26. C2×#14556532 | C4 | semidirect |
| 28. C2×D16×C73 | C4 | semidirect |
| 54. C2×Dic292 | C2×C4 | semidirect |
| 68. C2×#11924003 | C2×C4 | semidirect |
| 70. C2×D8×C73 | C2×C4 | semidirect |
| 72. C2×C16×C73 | C2×C4 | semidirect |
| 197. C73 | #13033 | semidirect |
| 206. C2×D16 | #64408 | semidirect |
| 234. C2×D8 | C2×#64408 | semidirect |
| 253. C2×C16 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626690 | 2 |
| #22626252 | 2 |
| #22626240 | 2 |
| #22626088 | 2 |
| #22624999 | 2 |
| #22624980 | 2 |
| C2×#17989021 | 2 |
| #13033 | 73 |