Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22619647 | C2 | semidirect |
| 3. #22619594 | C2 | semidirect |
| 4. #22611660 | C2 | semidirect |
| 5. #22611560 | C2 | semidirect |
| 6. #22608029 | C2 | semidirect |
| 7. C2×#360×C73 | C2 | semidirect |
| 66. C2×#11924003 | D4 | semidirect |
| 68. #14556527 | D4 | semidirect |
| 78. C2×Q16×C73 | D4 | semidirect |
| 80. C2×D8×C73 | D4 | semidirect |
| 230. C2×#360 | D73 | semidirect |
| 234. C73 | #13318 | semidirect |
| 277. C2×Q16 | D292 | semidirect |
| 281. 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 |
| #22619647 | 2 |
| #22619594 | 2 |
| #22611660 | 2 |
| #22611560 | 2 |
| #22608029 | 2 |
| C2×#360×C73 | 2 |
| #13318 | 73 |