Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | C22⋊Q8×C47 | C2 |
| prime radical | C2×C22⋊D47 | C22 |
| hypercenter | C22⋊Q8 | D47 |
| hypocenter | C47 | D4×Q8 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic94 | C2 | semidirect |
| 2. C2×Q8×D47 | C2 | semidirect |
| 3. #13094023 | C2 | semidirect |
| 4. #13094022 | C2 | semidirect |
| 5. #13094004 | C2 | semidirect |
| 6. #13094002 | C2 | semidirect |
| 7. #13094001 | C2 | semidirect |
| 8. #13093989 | C2 | semidirect |
| 11. C22⋊Q8×C47 | C2 | semidirect |
| 45. C22⋊D47 | Q8 | semidirect |
| 57. Dic94 | D4 | semidirect |
| 60. C22×C47 | C2×Q8 | semidirect |
| 64. C2×D47 | C2×Q8 | semidirect |
| 73. Dic47 | C2×Q8 | semidirect |
| 80. C47 | D4×Q8 | semidirect |
| 88. C22⋊Q8 | D47 | semidirect |
| 143. C22 | Q8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic94 | 2 |
| C2×Q8×D47 | 2 |
| #13094023 | 2 |
| #13094022 | 2 |
| #13094004 | 2 |
| #13094002 | 2 |
| #13094001 | 2 |
| #13093989 | 2 |
| C4×C22⋊D47 | 2 |
| (C22⋊D47)⋊C4 | 2 |
| C22⋊Q8×C47 | 2 |
| D4×Q8 | 47 |