Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
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×#14583340 | C2 | semidirect |
| 3. C2×#14583154 | C2 | semidirect |
| 4. C2×#14582710 | C2 | semidirect |
| 5. C2×#14582680 | C2 | semidirect |
| 6. #19132700 | C2 | semidirect |
| 7. C43×#2141 | C2 | semidirect |
| 60. #13063265 | D4 | semidirect |
| 63. #13063257 | D4 | semidirect |
| 73. C2×Q16×C43 | D4 | semidirect |
| 210. #2141 | D43 | semidirect |
| 242. C43 | #13317 | semidirect |
| 256. C2×Q16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583340 | 2 |
| #19144205 | 2 |
| C2×#14583154 | 2 |
| C2×#14582710 | 2 |
| C2×#14582680 | 2 |
| #19132700 | 2 |
| C43×#2141 | 2 |
| #13317 | 43 |