Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 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. #19144311 | C2 | semidirect |
| 2. #19144239 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. #19136331 | C2 | semidirect |
| 5. #19136224 | C2 | semidirect |
| 6. #19132710 | C2 | semidirect |
| 7. C2×C43×#509 | C2 | semidirect |
| 54. #13063261 | D4 | semidirect |
| 66. C2×Q16×C43 | D4 | semidirect |
| 74. C2×D8×C43 | D4 | semidirect |
| 79. M32×C43 | D4 | semidirect |
| 205. C2×#509 | D43 | semidirect |
| 242. C43 | #13310 | semidirect |
| 255. C2×Q16 | C22⋊D43 | semidirect |
| 263. C2×D8 | C22⋊D43 | semidirect |
| 283. M32 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144311 | 2 |
| #19144239 | 2 |
| C2×#14582712 | 2 |
| #19136331 | 2 |
| #19136224 | 2 |
| #19132710 | 2 |
| C2×C43×#509 | 2 |
| #13310 | 43 |