Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 566 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. #22627175 | C2 | semidirect |
| 2. #22627081 | C2 | semidirect |
| 3. #22627051 | C2 | semidirect |
| 4. #22627049 | C2 | semidirect |
| 5. #22626943 | C2 | semidirect |
| 6. #22626938 | C2 | semidirect |
| 79. #14556619 | C8 | semidirect |
| 81. #14556617 | C8 | semidirect |
| 82. #14556616 | C8 | semidirect |
| 87. AGL(1,ℤ/8)×C73 | C8 | semidirect |
| 134. C2×D292 | C2×C8 | semidirect |
| 150. #11924012 | C2×C8 | semidirect |
| 154. C2×D4×C73 | C2×C8 | semidirect |
| 157. M16×C73 | C2×C8 | semidirect |
| 188. Q8×C73 | C22⋊C8 | semidirect |
| 192. D4×C73 | C22⋊C8 | semidirect |
| 205. D292 | C22⋊C8 | semidirect |
| 214. Dic146 | C22⋊C8 | semidirect |
| 265. C73 | #8954 | semidirect |
| 299. AGL(1,ℤ/8) | #10596842 | semidirect |
| 362. C2×D4 | C2×#10596842 | semidirect |
| 386. M16 | C2×#10596842 | semidirect |
| 426. Q8 | C22⋊#10596842 | semidirect |
| 439. D4 | C22⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627175 | 2 |
| #22627081 | 2 |
| #22627051 | 2 |
| #22627049 | 2 |
| #22626943 | 2 |
| #22626938 | 2 |
| AGL(1,ℤ/8)×#64408 | 2 |
| #8954 | 73 |