Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#17989028 | C2 | semidirect |
| 3. C2×#17988842 | C2 | semidirect |
| 4. C2×#17988398 | C2 | semidirect |
| 5. C2×#17988368 | C2 | semidirect |
| 6. #22608036 | C2 | semidirect |
| 7. C73×#2141 | C2 | semidirect |
| 60. #14556531 | D4 | semidirect |
| 63. #14556523 | D4 | semidirect |
| 73. C2×Q16×C73 | D4 | semidirect |
| 216. #2141 | D73 | semidirect |
| 219. C73 | #13317 | semidirect |
| 256. C2×Q16 | D292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989028 | 2 |
| #22619541 | 2 |
| C2×#17988842 | 2 |
| C2×#17988398 | 2 |
| C2×#17988368 | 2 |
| #22608036 | 2 |
| C73×#2141 | 2 |
| #13317 | 73 |