Finite Group DatabasebetaFinite Group DatabasebetaOrder 29312.
420 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C229 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C229 |
| prime radical | C22×D4×C229 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C229 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #401×C229 | C2 | semidirect |
| 2. #399×C229 | C2 | semidirect |
| 3. #396×C229 | C2 | semidirect |
| 5. #389×C229 | C2 | semidirect |
| 6. #388×C229 | C2 | semidirect |
| 7. #388×C229 | C2 | semidirect |
| 77. C229 | #2801 | direct (N × H) |
| 78. #2801 | C229 | direct (N × H) |
| 79. #401 | C2×C229 | semidirect |
| 80. #399 | C2×C229 | semidirect |
| 81. #396 | C2×C229 | semidirect |
| 83. #389 | C2×C229 | semidirect |
| 84. #388 | C2×C229 | semidirect |
| 85. #388 | C2×C229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #401×C229 | 2 |
| #399×C229 | 2 |
| #396×C229 | 2 |
| #394×C229 | 2 |
| #389×C229 | 2 |
| #388×C229 | 2 |
| #2801 | 229 |