Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22623065 | C2 | semidirect |
| 2. C2×#17989022 | C2 | semidirect |
| 3. #22620417 | C2 | semidirect |
| 4. #22611666 | C2 | semidirect |
| 5. #22611646 | C2 | semidirect |
| 6. #22608017 | C2 | semidirect |
| 7. C73×#1976 | C2 | semidirect |
| 65. #14556531 | D4 | semidirect |
| 67. C2×#11924003 | D4 | semidirect |
| 73. C2×Q16×C73 | D4 | semidirect |
| 75. C2×D8×C73 | D4 | semidirect |
| 223. #1976 | D73 | semidirect |
| 225. C73 | #13334 | semidirect |
| 265. C2×Q16 | D292 | semidirect |
| 277. C2×D8 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623065 | 2 |
| C2×#17989022 | 2 |
| #22620417 | 2 |
| #22611666 | 2 |
| #22611646 | 2 |
| #22608017 | 2 |
| C73×#1976 | 2 |
| #13334 | 73 |