Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
492 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 92 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. #22626241 | C2 | semidirect |
| 3. C2×#17989500 | C2 | semidirect |
| 5. #22625007 | C2 | semidirect |
| 6. #22624994 | C2 | semidirect |
| 25. #17988863 | C4 | semidirect |
| 26. #17988862 | C4 | semidirect |
| 29. #17988859 | C4 | semidirect |
| 32. #473×C73 | C4 | semidirect |
| 60. C2×Dic292 | C2×C4 | semidirect |
| 78. #14556527 | C2×C4 | semidirect |
| 84. C2×Q16×C73 | C2×C4 | semidirect |
| 86. #108×C73 | C2×C4 | semidirect |
| 237. C73 | #12997 | semidirect |
| 249. #473 | #64408 | semidirect |
| 278. C2×Q16 | C2×#64408 | semidirect |
| 306. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626586 | 2 |
| #22626241 | 2 |
| C2×#17989500 | 2 |
| #22626171 | 2 |
| #22625007 | 2 |
| #22624994 | 2 |
| #473×D73 | 2 |
| #12997 | 73 |