Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14583340 | C2 | semidirect |
| 3. C2×#14582708 | C2 | semidirect |
| 4. #19136315 | C2 | semidirect |
| 5. C2×#14582681 | C2 | semidirect |
| 6. #19132702 | C2 | semidirect |
| 7. C2×C43×#470 | C2 | semidirect |
| 50. #13063265 | D4 | semidirect |
| 64. C2×Q16×C43 | D4 | semidirect |
| 79. #106×C43 | D4 | semidirect |
| 208. C2×#470 | D43 | semidirect |
| 242. C43 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D43 | semidirect |
| 289. #106 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583340 | 2 |
| #19144204 | 2 |
| C2×#14582708 | 2 |
| #19136315 | 2 |
| C2×#14582681 | 2 |
| #19132702 | 2 |
| C2×C43×#470 | 2 |
| #13317 | 43 |