Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#16838535 | C2 | semidirect |
| 3. C2×#21439884 | C2 | semidirect |
| 4. C2×#21439880 | C2 | semidirect |
| 5. C2×C22⋊(C239⋊C8) | C2 | semidirect |
| 6. #29504534 | C2 | semidirect |
| 7. C2×C22⋊Q8×C239 | C2 | semidirect |
| 46. C2×C239⋊C8 | D4 | semidirect |
| 56. C2×Q8×C239 | D4 | semidirect |
| 69. C4⋊C4×C239 | D4 | semidirect |
| 94. C23×C239 | SD16 | semidirect |
| 157. C239 | #2000 | semidirect |
| 160. C2×C22⋊Q8 | D239 | semidirect |
| 194. C2×Q8 | C22⋊D239 | semidirect |
| 226. C4⋊C4 | C22⋊D239 | semidirect |
| 242. C23 | #16838535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16838535 | 2 |
| C2×#21439934 | 2 |
| C2×#21439884 | 2 |
| C2×#21439880 | 2 |
| C2×C22⋊(C239⋊C8) | 2 |
| #29504534 | 2 |
| C2×C22⋊Q8×C239 | 2 |
| #2000 | 239 |