Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #1619 |
| commutator, Frattini, cosocle | C4×C8 | C23×C47 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C4×C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#3291 | C2 | semidirect |
| 2. C47×#2213 | C2 | semidirect |
| 3. C47×#1721 | C2 | semidirect |
| 4. C47×#1359 | C2 | semidirect |
| 5. C47×#1336 | C2 | semidirect |
| 9. C47×#493 | C22 | semidirect |
| 16. C47×#364 | C22 | semidirect |
| 18. C47×#322 | C22 | semidirect |
| 59. Q16×C47 | D8 | semidirect |
| 69. D8×C47 | D8 | semidirect |
| 103. #12314 | C47 | direct (N × H) |
| 116. #3291 | C2×C47 | semidirect |
| 117. #2213 | C2×C47 | semidirect |
| 118. #1721 | C2×C47 | semidirect |
| 119. #1359 | C2×C47 | semidirect |
| 120. #1336 | C2×C47 | semidirect |
| 129. #493 | C22×C47 | semidirect |
| 136. #364 | C22×C47 | semidirect |
| 138. #322 | C22×C47 | semidirect |
| 139. C47 | #12314 | direct (N × H) |
| 180. Q16 | D8×C47 | semidirect |
| 190. D8 | D8×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3291 | 2 |
| C47×#2213 | 2 |
| C47×#1721 | 2 |
| C47×#1359 | 2 |
| C47×#1336 | 2 |
| #12314 | 47 |