Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14583334 | C2 | semidirect |
| 2. #19144311 | C2 | semidirect |
| 3. #19144244 | C2 | semidirect |
| 4. C2×#14582713 | C2 | semidirect |
| 5. #19136222 | C2 | semidirect |
| 6. #19132711 | C2 | semidirect |
| 7. C43×#2145 | C2 | semidirect |
| 59. #13063265 | D4 | semidirect |
| 62. #13063261 | D4 | semidirect |
| 71. C2×Q16×C43 | D4 | semidirect |
| 73. C2×D8×C43 | D4 | semidirect |
| 209. #2145 | D43 | semidirect |
| 242. C43 | #13310 | semidirect |
| 255. C2×Q16 | D172 | semidirect |
| 263. C2×D8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583334 | 2 |
| #19144311 | 2 |
| #19144244 | 2 |
| C2×#14582713 | 2 |
| #19136222 | 2 |
| #19132711 | 2 |
| C43×#2145 | 2 |
| #13310 | 43 |